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. iaM wh

    I What is the Meaning of the Schrödinger Equation?

    I would like to discuss the Schrödinger equation in order to get some insight. The equation, as I understand it, is essentially an expression of the conservation of energy. What it says is that ∆Total Energy= ∆ Kinetic Energy + ∆ Potential Energy. In Schrödinger's day, there were various...
  2. patrykh18

    I Numerical solution to the Schrodinger eqn. using Finite Difference Method

    As part of my project I was asked to use the finite difference method to solve Schrodinger equation. I see how you can turn it into a matrix equation, but I don't know how to solve it if the energy eigenvalues are unknown. Are there any recommended methods I can use to determine those...
  3. M

    Non trivial solution to Schrödinger equation for 1-D infinite well

    Hello, I am trying to find the solution of Schrödinger equation on matlab. However, when I apply boundary conditions, MATLAB only gives me the solution with both coefficients 0. I want to find the solution : Asin(n*pi*x/L) You can see my code below. Could you please tell me where is my mistake...
  4. A

    I Can I use the Schrodinger picture when the Hamiltonian is time-dependent?

    In the Schrodinger picture, the operators don't change with the time, but the states do. So, what happen if my hamiltonian depend on time? Should I use the others pictures in these cases?
  5. Z

    Show that this Equation Satisfies the Schrodinger Equation

    I apologize for the bad formatting: To start off, I'm trying to use the Schrodinger Equation in the form: (ħ/2m) d^2Ψ(x,t)/dx^2+V(x,t)Ψ(x,t)=EΨ(x,t) I couldn't remember if I need to also take the partial derivative with respect to T as well, but I started off with just X. I plugged in my...
  6. G

    I General solution to the Time-independent Schrödinger equation?

    Has anyone formulated a general solution to the time-independent Schrödinger equation in terms of the potential function V(r), and if so, what is it? For any type of V(r). So, instead of a differential equation, a direct relationship between the wavefunction and the potential.
  7. H

    I Symmetry transformation in Heisenberg vs Schrödinger Picture

    Symmetry transformations are changes in our point of view that preserve the possible outcomes of experiment: $$\Psi \rightarrow U(\Lambda) \Psi$$ In the Heisenberg picture, observables in a fixed reference frame evolve according to: $$P(t) = U^\dagger (t)PU(t)$$ while in the Schrodinger...
  8. Auto-Didact

    A Schrödinger Evolution of Self-Gravitating Disks

    This paper was recently published in the Monthly Notices of the Royal Astronomical Society. Batygin 2018, Schrödinger Evolution of Self-Gravitating Disks I am posting this in here, but I am actually more interested in the implications of looking at this the other way around: namely, from a...
  9. entropy2information

    Schrodinger's Cat and The Universe

    I had a question about Schrodinger's cat that extends to the universe. First, I'm sure everyone knows the Schrodinger's cat set up so I won't repeat it. I will just ask, how can the cat be dead or alive prior to measurement? This measurement would be either atoms in the radioactive substance...
  10. learn.steadfast

    I Novel Schrodinger equation examples for 1D

    I've been studying the 1D schrodinger equation, and getting a feel for solutions in the harmonic oscillator, or potentials of inverse radius (atomic/hydrogen), and many versions of stair-step/ square potentials (square wells.) But, I've noticed that there are very few exact 1D potentials in the...
  11. Baynie

    MATLAB Code: Stationary Schrodinger EQ, E Spec, Eigenvalues

    Hello everyone, For weeks I have been struggling with this quantum mechanics homework involving writing a code to determine the energy spectrum and eigenvalues for the stationary Schrodinger equation for the harmonic oscillator. I can't find any resources anywhere. If anyone could help me get...
  12. Konte

    I About the Schrödinger equation

    Hi everybody, For solving the time dependent Schrödinger equation ##H|\psi(t) \rangle = i\hbar \frac{\partial}{\partial t}|\psi (t)\rangle##, I read in quantum mechanics books the assumption about the solution ##|\psi(t) \rangle## which is made of a linear combination of a complete set of the...
  13. stevendaryl

    A Question about equivalence of Path Integral and Schrodinger

    I've seen a proof that the path integral formulation of quantum mechanics is equivalent to solving Schrodinger's equation. However, it appears to me that the proof actually depended on the Hamiltonian having a particular form. I'm wondering how general is the equivalence. Let me sketch a...
  14. S

    Prove that ##\psi## is a solution to Schrödinger equation

    Homework Statement For a wavefunction ##\psi##, the variance of the Hamiltonian operator ##\hat{H}## is defined as: $$\sigma^2 = \big \langle \psi \mid (\hat{H} - \langle\hat{H}\rangle)^2 \psi \big\rangle$$ I want to prove that if ##\sigma^2 = 0##, then ##\psi## is a solution to the...
  15. Glenn Rowe

    A Evolution operator in QFT - why Schrodinger?

    I'm reading through a couple of books (Lahiri & Pal's "A First Book of Quantum Field Theory" and Greiner & Reinhardt's "Field Quantization" and have come to the derivation of the evolution operator which leads to the S-matrix. In both books, the derivation starts with the Schrodinger equation in...
  16. J

    I What is the Difference between the lottery and QM?

    It seems to me that so far in quantum mechanics, because we have yet to establish probability patterns for, say, what the spin of a photon is, we have made it some mystical thing that we can only know by measuring it. I don't really buy that; is the result of a lottery impossible to know until...
  17. X

    Energy of Hydrogen 1s using simplified Schrodinger equation

    Homework Statement [/B] The Hamiltonian and wavefunction for the ground state of the hydrogen atom H(1s1) are given, in atomic units, as ## \hat {H} = - \frac{1}{2} \nabla^2 - \frac {1}{r} ## and ## \phi(1s) = \sqrt {\frac {1}{\pi }} e^{-r} ## . Using the radial portion of the Laplacian in the...
  18. hilbert2

    A How Does a Particle's Energy State Change in a Non-Uniform 2D Corridor?

    Suppose we have a particle of mass ##m## moving freely in the xy-plane, except for being constrained by hard walls to have ##-L/2 < y < L/2##. Now, the energy eigenstates would be something like ##\psi (x,y) = C \psi_x (x) \psi_y (y) = C e^{-ikx}\cos\left(\frac{n\pi y}{L}\right) ##, where...
  19. B

    A Nonlinear Schrodinger equation and linearity of Q.M.

    Hello all, you may already know that Q.M. is a linear theory however there is something called nonlinear Sch. eq. for example Gross-Pitaevskii equation. How can such a thing exist considering that Q.M. is a strictly linear theory. Cheers.
  20. B

    I "Derivation" of the Schrödinger Equation

    When reading a textbook I came across some reasoning about Schrödinger Equation. It started with the wave function $$\nabla^2\psi=k^2\psi$$ I am a bit lost at this point. Where does the right side of the equation come from? What should I review to fix that part of my knowledge?
  21. AuxPart

    I Does the Schrödinger equation link position and momentum?

    I recently found this article about the dynamics of the wave function. It has some good simple illustrations and I found it valuable. But the author has a question himself, about understanding the Schrodinger equation. I wonder if anybody here could fill in the missing piece. The relevant part...
  22. B

    I Can the Schrodinger equation satisfy Laplace's equation?

    The time-dependent Schrodinger equation is given by: ##-\frac{\hslash^{2}}{2m}\triangledown^{2}\psi+V\psi=i\hslash\frac{\partial }{\partial t}\psi## Obviously, there is a laplacian in the kinetic energy operator. So, I was wondering if the equation was rearranged as...
  23. nomadreid

    I Hamiltonian in Schrödinger: necessarily total energy?

    This is a basic question, so probably easy to answer. The following from Wikipedia seems pretty standard while describing the Schrödinger equation: "...and Ĥ is the Hamiltonian operator (which characterises the total energy of the system under consideration)." On the other hand, from page 100 of...
  24. bluejay27

    A What form of the Schrodinger equation do you use for intensity?

    I am trying to see how I can use the schrodinger equation to quantify the changes in the intensity of light. My closest guess is using the time dependent pertubation theory
  25. B

    Schrodinger equation and boundary conditions

    Hi at all, I'm tring to solve Schrodinger equation in spherically symmetry with these bondary conditions: ##\lim_{r \rightarrow 0} u(r)\ltimes r^{l+1}## ##\lim_{r \rightarrow 0} u'(r)\ltimes (l+1)r^{l}## For eigenvalues, the text I'm following says that I have to consider that the...
  26. V

    I I am interested in Schrodinger equation with tempor. element

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  27. B

    Comp Sci [C++] Schrodinger equation solver and nuclear density

    Hi everybody! I need to compute a C++ program for solve Schrodinger equation and calculate nuclear density. My nucleus is made up of only neutrons immersed in a potential of a harmonic oscillator. Schrodinger equation is: $$[-\frac{\hbar^2}{2m}\triangledown^2+V_{HO}(r)]\psi=E\psi$$ with...
  28. SemM

    I What are the limits of the boundaries for the Schrödigner equation

    If one considers the quantized levels of E, for the solutions to the Schrödinger eqn,, then I am wondering: what are the lowest possible energies that can occur for the Schrödinger eqn? I take the highest possible energy is at the classical limit, but is the zero-point energy the absolute...
  29. A

    I Understanding Gauge Symmetry: A Review of the Schrödinger Equation

    I have reviewed the various posts on gauge symmetry in particular this one which is now closed. In this post there is the following link:http://www.vttoth.com/CMS/physics-notes/124-the-principle-of-gauge-invariance. This is a good read. However, there is some clarification I need. The...
  30. B

    Schrodinger equation in cylindrical coordinates.

    Hi guys! For nuclear case, I need to write an Schrodinger equation in cylindrical coordinates with an total potential formed by Woods-Saxon potential, spin-orbit potential and the Coulomb potential. Schrodinger equation can be written in this form: $$[-\frac{\hbar^2}{2m}(\frac{\partial...
  31. SemM

    I Solving the Schrödinger eqn. by commutation of operators

    Hi, I noticed that the raising and lowering operators:\begin{equation} A =\frac{1}{\sqrt{2}}\big(y+\frac{d}{dy}\big) \end{equation}\begin{equation} A^{\dagger}=\frac{1}{\sqrt{2}}\big(y-\frac{d}{dy}\big) \end{equation}can be used to solve the eqn HY = EY However I am curious about something...
  32. S

    A Solving the Schrödinger equation for free electrons

    Dear all, sorry I made a new post similar to the previous post "Initial conditions..", however, a critical point was missed in the previous discussion: The initial conditions y(0)=1 and y'(0)=0 are fine and help in solving the Schrödinger equation, however, studying free electrons, the equation...
  33. S

    A What are typical initial conditions for the Schrödinger eq?

    Hi, I am wondering if there exists some general initial conditions for solving the Schödinger eqn. for 1D free electrons ? Thanks!
  34. J

    B The deduction of Schrodinger equation, I'm stuck

    Hi everyone! Please, I'm trying to understand the Schrodinger equation, and I've understood it this far, which which is a miracle, hehehe: (Laplacian)(psi) plus ((2phi)/h)^2.2m (E-V)(psi) I know that hbar = h/(2phi) But how that turns into (Laplacian)(psi)+2m/(hbar)^2.(E-V)(psi) My math...
  35. snoopies622

    I About the premises behind the Schrödinger equations

    Long ago I read on these forums that one cannot derive the Schrödinger equations because they're fundamental scientific laws. But I have noticed that I can generate them by making the following physical assumptions and then doing a trivial amount of substitution and differentiation: (1) \frac...
  36. V

    B Schrödinger Equation for the fusion of Deuterium(2H) and a Proton(H)

    In fact I am not sure if this is the right place to ask such a question but I'm going to ask anyways, just tell me if I am in the wrong place. So I doing a little experiment with the Schröndinger's equation, but the problem is I can't find a certain function. You all know the Schrödingers...
  37. O

    Show that this plane wave satisfies the Schrödinger Eqn

    Homework Statement I'm asked to show that the two dimensional plane wave (for constant C) \psi \left ( \mathbf{r} \right )=Ce^{-i\mathbf{k}\cdot \mathbf{r}} satisfies the Schrödinger equation: -\frac{\hbar^{2}}{2m_e}\frac{\mathrm{d}^2 \psi\left ( \mathbf{r} \right )}{\mathrm{d}...
  38. J

    I Schrodinger equation and Heisenberg equation of motion

    My question is that how does the Schrodinger equation arise from the Heisenberg equation of motion in the quantum field formalism. These are from Hatfield's book. So I'm having some difficulties to reproduce (2.36) by plugging (2.55) into (2.37) primarily because H is an integral...
  39. O

    Time independent Schrödinger Eqn in a harmonic potential

    Homework Statement I am currently reading a textbook on solving the Schrödinger equation for the harmonic oscillator using the series method; $$-\frac{\hbar^{2}}{2m}\frac{\mathrm{d}^2 \psi }{\mathrm{d} x^2}+\frac{1}{2}m\omega ^{2}x^2\psi =E\psi $$ It starts by using these two dimensionless...
  40. C

    I Deductions of Formulas for Energy

    So, I am a newbie in quantum mechanics, took modern physics last fall for my physics minor. I know that Schrodinger based his equation based on the equation K + V = E, by using non-relativistic kinematic energy (P2/2m + V = E) p becoming the operator p= -iħ∇ for the wave equation eigenfunction...
  41. W

    Time-independent Schrödinger equation, normalizing

    Homework Statement An electron coming from the left encounters/is trapped the following potential: -a<x<0; V=0 0<x<a; V=V0 infinity elsewhere the electron has energy V0 a)Write out the wave function b)normalize th wave function Homework EquationsThe Attempt at a Solution for -a<x<0...
  42. D

    I Kinetic and Potential energy operators commutation

    Hi All, Perhaps I am missing something. Schrodinger equation is HPsi=EPsi, where H is hamiltonian = sum of kinetic energy operator and potential energy operator. Kinetic energy operator does not commute with potential energy operator, then how come they share the same wave function Psi? The...
  43. C

    Solving a Piecewise Schrodinger equation

    Homework Statement I was trying to solve the time-independent Schrodinger's equation for this well: http://i.imgur.com/C9QrvkX.png First I tried to look at cases where the energy of a particle is ##E < V_1##. Homework Equations Schrodinger's equation...
  44. W

    Schrodinger time independent equation for steps and barriers

    Ok for starters, I am sorry for the length of the question and jamming multiple questions in here i feel like my doubts are all related and it would be best just to put it all in one place instead of creating 2-4 topics. I'm beginning to feel confused with the amount of ways i see people...
  45. D

    A Bright, dark soliton for cubic-quintic nonlinear Schrodinger

    For a given stationary cubic-quintic nonlinear Schrodinger equation, EU=-U_XX+G1|U|^2U+G2 |U|^4 U, where X=X(t,x). There are bright and dark solitons. In many references, it is found that there is typo or mistake in dark soliton by substituting their soliton solution to this above eqaution. The...
  46. M

    Nonlinear Schrodinger Equation Dispersion Relation

    The Nonlinear Schrodinger Equation (NSE) is presented as: $$i\frac{∂A}{∂z} = \frac{1}{2}β_2\frac{∂^2A}{∂t^2}-\gamma|A^2|A$$ The steady state solution $$A(z)$$ Can be derived as an Ansatz given by: $$ A(z) = \rho(z)e^{i\phi(z)}$$ By substituting and solving the ODE, the steady state...
  47. W

    I Time independent Schrodinger equation results (1D)

    okay so i need some help interpreting some of the results, so (-ħ2/2m)Ψ''=E-V0Ψ; So i set k2= 2m*(E-V0)/ħ2 and so : Ψ''=-k2Ψ so if V0=0 or is smaller than E, k2 is positive; *need for help starts here* Ψ=Aeikx+Be-ikx; another result for this would also be only eikx so is the second term only...
  48. D

    Question related to Schrodinger equation

    Homework Statement Homework EquationsThe Attempt at a Solution It is a short question so I don't suppose it is difficult. However, I don't really understand what it is asking for : 1.The TDSE itself is already a 2nd-order differential equation (if you substitute the terms back into H). 2...
  49. yecko

    Schrodinger equation and Born's Rule

    Homework Statement [/B] Q18. Which of the following statements about Schrodinger equation is true? A) The exact solution of the equation never exists B) It is only applicable to the hydrogen-like atoms C) We can know the energy of the atomic orbital by solving the equation D) The square of the...
  50. Docdan6

    Classical behavior, 3 dimension wave function and reflection

    Homework Statement I'm a pharmacologist and I have a modern physics course to do. This is not my field and I'm completely lost... We were given this problem to do. Thanks a lot in advance. Consider a potential where U(x) = 0 for x ≤ 0 U(x) = -3E for x > 0 Consider a particle of energy E...
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