What is Schrödinger: Definition and 611 Discussions

Erwin Rudolf Josef Alexander Schrödinger (UK: , US: ; German: [ˈɛɐ̯viːn ˈʃʁøːdɪŋɐ]; 12 August 1887 – 4 January 1961), sometimes written as Erwin Schrodinger or Erwin Schroedinger ("oe" is the proper transliteration of the German "ö"), was a Nobel Prize-winning Austrian-Irish physicist who developed a number of fundamental results in quantum theory: the Schrödinger equation provides a way to calculate the wave function of a system and how it changes dynamically in time.
In addition, he was the author of many works on various aspects of physics: statistical mechanics and thermodynamics, physics of dielectrics, colour theory, electrodynamics, general relativity, and cosmology, and he made several attempts to construct a unified field theory. In his book What Is Life? Schrödinger addressed the problems of genetics, looking at the phenomenon of life from the point of view of physics. He paid great attention to the philosophical aspects of science, ancient and oriental philosophical concepts, ethics, and religion. He also wrote on philosophy and theoretical biology. He is also known for his "Schrödinger's cat" thought experiment.

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  1. J

    Question about deriving TE Schrodinger WE

    To start, we have: ψ=e^{i(kx+wt)} ψ_x=ikψ ψ_{xx}=-k^2ψ λ=\frac{h}{p} k=\frac{2π}{λ} E=\frac{p^2}{2m}+V Then, multiply both sides of energy equation by ψ to get: Eψ=\frac{p^2}{2m}ψ+Vψ And replace -k^2 in the wave equation with -\frac{p^2}{hbar^2}. Then plug into energy equation for p^2 to get...
  2. D

    Application of Schrodinger equation to SHO

    when Schrodinger equation is applied to SHO only positive value of potential energy changes it to Hermitian polynomial and hence solution is possible but potential energy is positive only when the particle is moving away from the the mean position.The sign of potential is negative when the...
  3. M

    Time Dependent Schrodinger Equation

    Homework Statement Show that the wave function ##\Psi(x,t)=Asin(kx-ωt)## does not satisfy the time dependent Schrodinger Equation. Homework Equations ##-\frac{\hbar}{2m}\frac{\partial^2\psi(x,t)}{{\partial}x^2}+V(x,t)\psi(x,t)=i\hbar\frac{\partial\psi(x,t)}{{\partial}t}## The...
  4. 2

    General solution of the Schrodinger equation for a free particle?

    Homework Statement I'm trying to figure out how the general solution of the Schrodinger equation for a free particle when v=0 relates to anything I have learned in class...Homework Equations For Eψ=(hbar2/2m)d2ψ/dx2The Attempt at a Solution I really have no idea- what is confusing me is that ψ...
  5. K

    Solution to Schrodinger Equation

    Homework Statement I need Part B of this question http://physics.wustl.edu/classes/FL2013/217/homework/ps03.pdf Recall that the free particle Schr¨odinger equation, i~ ∂ ∂tψ(x, t) = − ~ 2 2m ∂ 2 ∂x2 ψ(x, t) (1) has solutions of the “plane wave” form ψk(x, t) = exp[ikx − iω(k)t] , (2) where...
  6. L

    Schrodinger Equation and 1D Box

    Homework Statement Trying to construct Shrodinger Equation given: * mass: m * Boundary Conditions: (potential) V(x)=-Vo exp(-x/L) for 0<x≤L V(x)=∞ for x≤0 Homework Equations The Attempt at a Solution (-h^2 / 2m ) (d^2 ψ / dx^2) + V(x)ψ = E * psi Not sure how to incorporate...
  7. M

    Weak Form of the Effective Mass Schrodinger Equation

    Hi, I am numerically solving the 2D effective-mass Schrodinger equation \nabla \cdot (\frac{-\hbar^2}{2} c \nabla \psi) + (U - \epsilon) \psi = 0 where c is the effective mass matrix \left( \begin{array}{cc} 1/m^*_x & 1/m^*_{xy} \\ 1/m^*_{yx} & 1/m^*_y \\ \end{array} \right) I know that...
  8. A

    How do we *know* the Schrodinger equation for H2+ can't be solved?

    In all the introductions to the Born-Oppenheimer approximation I've seen, they make the following claim: "If you write out the stationary Schrodinger equation for the simplest molecule -- H_2^+ -- even it cannot be solved analytically, so we are forced to make an approximation." But how do we...
  9. M

    Numerical solution of one dimensional Schrodinger equation

    Hi, I want to solve one dimensional Schrodinger equation for a scattering problem. The potential function is 1/ ( 1+exp(-x) ). So at -∞ it goes to 0 and at ∞ it's 1. The energy level is more than 1. I used Numerov's method and integrated it from +∞ (far enough) backwards with an initial value...
  10. hideelo

    Angular momentum in the 3D Schrodinger eqn with a central force

    I guess this question can apply in all the generality of the 3D Schrodinger eqn. with a central force, the case I'm thinking of however is the the hydrogen atom. When solving the equation, we derive the quantization of the angular momentum, which has me thinking that before we begin quantizing...
  11. E

    Solution to the 1D Free Schrodinger Equation

    So starting from the time dependent schrodinger equation I perform separation of variables and obtain a time and spatial part. The spatial part is in effect the time independent schrodinger equation. Since we are dealing with a free particle I can take the time independent equation, set V = 0...
  12. M

    Left hand side of the Schrödinger equation

    The time dependent Schrödinger equation is: i\hbar\partial_{t}\Psi=\hat{H}\Psi Does it mean that the operator i\hbar\partial_{t} has the same eigenstates and eigenvalues as any Hamiltonian?
  13. M

    Form of Solution to Schrodinger Equation

    Hey guys, I just want to ask on how do you determine the form of wave function for Schrodinger equation of finite potential well and potential barrier. Why is it ψ(x) = Ae^ikx + Be^-ikx (x < -a) ψ(x) = Fe^ikx (x > a) ψ(x) = Ce^μx + De^-μx (-a < x < a) for k^2 =...
  14. M

    Schrödinger Equations in three dimensions

    I've come to the point in my homework discussing the above, and more specifically, energy levels, wave functions, excited states etc.. And while I can locate an appropriate formula and plug-n-chug, I'm finding that I have no clue what these equations and numbers actually mean. And(in my...
  15. G

    'Largest' Schrodinger cat states created to date?

    Hey, I've been searching around for papers reporting on the creation of relatively large cat states, the largest I have been able to find are by Wineland, and are on the scale of nano meters. Does anyone know of any articles where such states have been created (experimentally) and reported...
  16. U

    Delta function potential; Schrodinger Equation

    Homework Statement Consider the TISE for a particle of mass m moving along the x-axis and interacting an attractive delta function potential at origin: Part(a): What is the difference between a bound state particle and a free particle? Part(b): Show ##\psi _{(x)} = exp (-|k|x)## is a...
  17. M

    QM solutions to the Schrodinger Equation

    Homework Statement Here's something that's confusing me. Say we have a potential V(x) = Vo if x < 0, x > a and V(x) = 0 if 0 < x < a (yes I know the notation with greater than/equals etc isn't totally correct, but you know what I'm talking about.) In the middle section, ψ'' +...
  18. Runei

    Time-independence of seperable solutions of the Schrödinger eqn

    Hey there clever folk, So I am taking a class in Quantum Mechanics, and I've just completed an assignment about seperable solutions to the schrödinger equation. One of the questions was to show that seperable solutions give rise to time-independent probability densities. So I was having the...
  19. W

    How do we know E is energy in the time-independent Schrodinger eq

    Hi everyone, One approach to solve the Schrodinger equation is to use separation of variables: the solution is composed of a time dependant and space dependant component. When we go through the math, we get a time dependent LHS equal to a space dependant RHS, which means they must both be...
  20. M

    Generalized Schrödinger equation

    This equation (see attachment) appears in one of Prof. Susskinds's lectures on Quantum Mechanics: in trying to differentiate the coefficients of the eigenvectors of a wave function with respect to time, an exponential e^(-iEt) is introduced for alpha. I can see that d/dt e^(-iEt) = -iE...
  21. D

    About the radial Schrödinger quation

    Dear all, I meet a difficult question as follows: -\frac{1}{ρ^{2}}\frac{d}{dρ}(ρ^{2}\frac{dR_{l}}{dρ})+[\frac{l(l+1)}{ρ^{2}}+V(ρ)]R_{l}(ρ)=ER_{l}(ρ) (1) let x=ln(ρ) and y=ρ^{1/2}R_{l}(ρ) ,then y^{''}=γy...
  22. R

    Schrodinger Equation in Spherical co-ordinates. Constants.

    When normalising the S.E. in spherical coordinates you split it up into 3 integrals, with respect to r, theta and phi. My question is, once you have found the constants for each, when writing out the normalised PSI do you simply place them as a product in the solution? i..e PSI...
  23. G

    Particle in a box Schrodinger equation

    I'm going though the particle in a box lesson in my physics textbook right now. I understand all the math, but don't understand a lot of the physics behind it. Also this is an intro physics course, we're only covering the basics of quantum mechanics and not going into too much detail. How come...
  24. A

    Dimensional Analysis - Schrödinger equation

    To illustrate the abstract reduction to dimensionless quantities apply it to the harmonic oscillator V(x) = (m \omega^2 x^2) / 2 using x_0 = sqrt(h-bar/(m \omega)) and fi nd a dimensionless Schrodinger equation. Translate the known solutions to the Schrodinger equation for the harmonic...
  25. D

    For the infinite square-well potential, schrodinger eqation

    Homework Statement For the infinite square-well potential, find the probability that a particle in its fourth excited state is in each third of the one-dimensional box: (0 to L/3) (L/3 to 2L/3) and (2L/3 to L) Homework Equations ∫ψ^2= ProbabilityThe Attempt at a Solution So from ∫ψ^2 for...
  26. K

    Initial condition for Schrödinger equation

    (If the equation below do not appear correctly, you can read all of the question in the attached file.) Solving the time dependent 1D Schrödinger equation, one can show that in all points (x,t), i\bar{h}\frac{\partial}{\partial t}\Psi(x,t)=-\frac{\bar{h}^2}{2m}\frac{\partial^2}{\partial...
  27. R

    Solving the time dependant schrodinger eqn in dirac (bra ket) notation

    given: at t=0 |PSI(0)> = 1/2 |PSI1> + (SQRT3)/2 |PSI2> --------------------------------------------------------------------- my attempt so far: we can write |PSI1> = 1/2 |UP> + 1/2 |DOWN> |PSI2> = (SQRT3)/2 |UP> + (SQRT3)/2 |DOWN> therefore |PSI(0)> = 1/2 |UP> + 1/2...
  28. A

    Question about finding quantom numbers N_(n) for Schrodinger Eqn in 3D

    I'm using the Modern Physics by Tipler (6th edition) book. In sec 7.1 it talks about the first excited state being either E_(112 ) E_(121 ) E_(112). My question is what is the process of finding the n_(1),n_(2),n_(3) quantum numbers ? How i understand you pick random values and from their find...
  29. H

    Energy From Schrodinger Equation

    Homework Statement Given \Psi(x, y, z)=(2/L)^{3/2}sin(\frac{n_x\pi x}{L})sin(\frac{n_y\pi y}{L})sin(\frac{n_z\pi z}{L}), calculate the first few energy levels and tell which are degenerate. The Attempt at a Solution I don't have much of an attempt to be honest.. What I've done so far...
  30. W

    The Schrodinger Equation: How to Solve for Time Evolution and Eigenstates

    I'm working my way through some QM problems for self-study and this one has stumped me. Given the Hamiltonian as H(t) = f(t)H^0 where f(t) is a real function and H^0 is Hermitian with a complete set of eigenstates H^0|E_n^0> = E_n^0|E_n^0>. Time evolution is given by the Schrodinger equation i...
  31. C

    Schrodinger half spin states expectation values

    Homework Statement What is the expectation value of \hat{S}_{x} with respect to the state \chi = \begin{pmatrix} 1\\ 0 \end{pmatrix}? \hat{S}_{x} = \frac{\bar{h}}{2}\begin{pmatrix} 0&1\\ 1&0 \end{pmatrix}Homework Equations <\hat{S}_{x}> = ∫^{\infty}_{-\infty}(\chi^{T})^{*}\hat{S}_{x}\chi...
  32. C

    Schrodinger solution spin half particles

    Homework Statement The evolution of a particular spin-half particle is given by the Hamiltonian \hat{H} = \omega\hat{S}_{z}, where \hat{S}_{z} is the spin projection operator. a) Show that \upsilon = \frac{1}{\sqrt{2}}\begin{pmatrix} e^{-i\frac{\omega}{2}t}\\ e^{i\frac{\omega}{2}t}...
  33. F

    Schrödinger theory, bunch of questions

    Hi, I've got a few questions about Schrödinger's formulation of QM, mostly about how to interpret the results: 1) How do I choose boundary conditions? I know that I should always normalize the wavefunction and make it continuous but some times you need to make the derivative continuous as...
  34. G

    What is wavefunction in the time-dependent schrodinger equation?

    Hello. The wave function or state vector (callled 'Ket') ψ in the time-dependent schrodinger equation i\hbar\frac{∂ψ}{∂t}=\widehat{H}ψ is the just energy eigenfunction or any wavefunction for the given system? For example, can ψ be momentum eigenfunction or angular momentum...
  35. M

    Solving the Schrodinger Equation for V(x)=A sech^2(αx)

    [b]1. How can I solve the Schrodinger equation for a potential V(x)= A sech^2(αx) ? How do I come to know that whether sech(αx) is a non-node bound state of the particular or not? [b]2. p^2/2m + V(x) = E [b]3. exp(kx)[A tanh(αx) + C]
  36. A

    Second quantization of the Schrodinger fields

    Hi, I'm reading www.phys.ethz.ch/~babis/Teaching/QFTI/qft1.pdf and trying to understand the canonical quantization of the Schrodinger field. In particular, the Lagrangian: \begin{equation} \mathcal{L} = \frac{i}{2}\psi^* \partial_0 \psi - \frac{i}{2}\psi \partial_0 \psi^* +...
  37. P

    Reducing angular Schrodinger equation to eigenvalue problem

    Homework Statement The angular part of the Schrodinger equation for a positron in the field of an electric dipole moment {\bf d}=d{\bf \hat{k}} is, in spherical polar coordinates (r,\vartheta,\varphi), \frac{1}{\sin\vartheta}\frac{\partial}{\partial\vartheta} \left( \sin\vartheta\frac{\partial...
  38. N

    Differential equations in the schrodinger equation.

    i got a book on differential equations that says a shortcut to solving the general differential equation f'(x)+p(x)f(x)=g(x) is to take the antiderivative of g(x) dx times exp(-p(x) dx times x) to solve for f(x) where dx represents the functions antiderivative. (i kno its supposed to represent...
  39. S

    Schrodinger equation in the reciprocal lattice.

    Hi Everybody, I am learning solid state physics using a German book called "Festkorperphysik" written by Gross and Marx. Now, in page 336 the Schrodinger equation in momentum space is introduced: \left( \frac{\hbar^2 k^2}{2m} - E \right) C_\vec{k} + \sum_\vec{G} V_\vec{G}...
  40. P

    Proving Parity in Normalized Solutions of the Schrodinger Equation

    Hopefully this is in the correct section. Struggling with this question though I don't think it should be particularly difficult: Show that if V(x) = V(-x) normalised solutions to the time-independent Schrodinger equation have definite parity - that is, u(x) = +-u(-x) (+- means plus or...
  41. snoopies622

    How to go from Heisenberg operators to Schrödinger operators

    It is obvious to me how \hat {x} = x; \hspace{5 mm} \hat {p}_x = -i \hbar \frac {\partial} {\partial x} implies [ \hat {x} , \hat {p}_x ] = i \hbar and I can accept that these two formulations are mathematically equivalent, but I do not know how in general (or even in this specific...
  42. C

    Schrodinger Equation for Constrained Particle

    Hi, I am confused about how we obtain a part of the Schrodinger equation for a particle of mass m that is constrained to move freely along a line between 0 and a. Equation: \frac{d^{2}ψ}{dx^{2}}+(\frac{8∏^{2}mE}{h^{2}})ψ(x)=0 Where does the value in the parenthesis come from and what...
  43. P

    Can we rewrite Schrodinger equation using observable variable?

    We know that in Schrodinger equation, Ψ is called wave function, which is not observable, while Ψ·Ψ* is the probability, which is observable. can we rewirte the Schrodinger equation to a form without Ψ but only Ψ·Ψ*? because I think, in this way can I figure out all conservations in the...
  44. B

    Schrodinger equation molecules

    How do I write a full Schrodinger equation, pre-approximation, for a mixture? Let's say 75% H2 and 25% He by number of particles. I already know the form and very basic applications of the Schrodinger equation and the Hamiltonian. What I want to know is, the specifics, such as how to specify...
  45. P

    Solutions to Time-dependent Schrodinger Equation

    I am reading David Griffiths' book on Quantum Mechanics, and he usually says that the general solution to the TDSE, given a potential V, can a DISCRETE linear combinations of the wavefunction solutions. However, in one section, he says that the linear discrete sum can be regarded as a continuous...
  46. S

    Schrödinger cat´s from Rovelli Relational Quantum Mechanics viewpoint

    From RQM point of view, the Scrödinger cat appears 50 % times alive and 50 % times dead. From cat himself point of view he is 50 % times alive and 50 % times dead. But when it dies, he observe his reality like dead (non consciousness about external reality) or alive (conscious)-consciousness of...
  47. B

    Variational Derivation of Schrodinger Equation

    In reading Weinstock's Calculus of Variations, on pages 261 - 262 he explains how Schrodinger apparently first derived the Schrodinger equation from variational principles. Unfortunately I don't think page 262 is showing so I'll explain the gist of it: "In his initial paper" he considers...
  48. PsychonautQQ

    Infinite Well with Schrodinger equation

    Homework Statement I'm having a bit of trouble following my textbook, I was under the impression ψ(x) = e^i(kx) = Cos(kx) + iSin(kx) but in my textbook they write the general solution to this equation as ψ(x) = ASin(kx) + BCos(kx). How come they wrote the sin part as not imaginary? isn't this...
  49. W

    Integrating the time-indepdent Schrodinger equation

    Homework Statement A particle of mass m is confined to move in a one-dimensional and Diract delta-function attractive potential V(x)=-\frac{\hbar^2}{m}\alpha\delta(x) where \alpha is positive. Integrate eh time-independent Schrodinger equation between -\epsilon and \epsilon. Let...
  50. C

    How to gain an understanding of the Schrodinger equation for a noob

    Should I start by learning about the equations for classical harmonic waves and how the de Brolier equations can be applied to them? What else should I learn? I'm a chemistry student and we did a class on quantum chemistry, but the mathematical side of it was way too complicated for me so I just...
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