What is Quantum mechahnics: Definition and 188 Discussions

Can an on board laser be used to propel a solar sail spacecraft if the laser is pointed at the sails ? Would Newtons third law affect the laser and maybe prevent the ship from moving ? Thank you for answering my very ignorant questions. NineNinjas911

Can anyone explain me ; - What is quantum entanglement and how it effects the space-time and matter in our universe??

Mentor note: Member warned that an attempt must be shown. 1. Homework Statement This question is from book Afken Weber, Mathematics for Physicist. An operator ##T(t + ε,t)## describes the change in the wave function from t to t + ##\epsilon## . For ##\epsilon## real and small enough so that...

When particles are shot at the plate/screen in the double slit experiment, why doesn't the particles interact with the screen? Shouldn't the plate act as an observer and "collapse" the wave function into one or the other slit? Why does it take a measuring apparatus to know which slit the...

hi guys i recently was reading about hawking radiation and how he overcome the lack of a theory for quantum gravity by using a mathematical trick ( to see the effect of gravity on quantum fields ) and this trick was the Bogoliubov transformation ... , i just want some one to briefly explain...

Homework Statement The Attempt at a Solution [/B] Hi All, I'm having trouble answering part (f) of the above question. I have managed parts (d) and (e) fine but am not sure how to proceed with part (f). I am pretty sure that the amplitude of the reflected wave in region 1 will be zero...

Hi physics forms! I'm practicing to for an Quantum mechanics exam, and i have a problem. 1. Homework Statement I have two problems, but it's all related to the same main task. I have a state for the Hydrogen: ## \Psi = \frac{1}{\sqrt{2}}(\psi_{100} + i \psi_{211})## where ## \psi_{nlm}##...

I am practicing old exams. I tried my best but looking at an old and a bit unreliable answer list, and i am not getting the same result. Homework Statement At time ##t=0## the nomralized harmonic oscialtor wavefunction is given by: ## \Psi(x,0) = \frac{1}{\sqrt{3}}(\psi_0(x) + \psi_1(x) + i...

I need to calculate the energy of the ground state of a helium athom with the variational method using the wave function: $$\psi_{Z_e}(r_1,r_2)=u_{1s,Z_e}(r1)u_{1s, Z_e}(r2)=\frac{1}{\pi}\biggr(\frac{Z_e}{a_0}\biggr)^3e^{-\frac{Z_e(r_1+r_2)}{a_0}}$$ with ##Z_e## the effective charge considered...

What is the nonperturbative approach to quantum mechanics as opposed to perturbative one? When does the latter method fail and one has to apply nonperturbative approach? Please keep your discussion confined within non-relativistic quantum mechanics.

Homework Statement A particle of energy E moves in one dimension in a constant imaginary potential -iV where V << E. a) Find the particle's wavefunction \Psi(x,t) approximating to leading non-vanishing order in the small quantity \frac{V}{E} << 1. b) Calculate the probability current density...

"Calculated the total magnetic moment of a hydrogen atom in the ground state in a weak magnetic field which arises from hyper fine splitting of the ground state. How many beams does hydrogen produce from a Stern-Gerlach analyzer with a weak magnetic field?" I've calculated the magnetic moments...

To whom it may concern, I am having issues with a given assignment in my quantum mechanics class. The instructions listed below are all I have to go on since the prof. is not available for discussion and I have searched through at least 15 articles regarding plane waves and a dozen textbooks...

Homework Statement Considering the atom made of an electron and a positron. The spin-orbit Hamiltonian is: $$H=\frac{e^2}{4\nu^2c^2r^34\pi\epsilon_0}\vec{L}\cdot\vec{S}$$ with ##\vec{L}## the relative angular momentum, with ##\vec{S}## the total spin and ##\mu## the reduced mass. Finding the...

Homework Statement Considering the molecule of ##C_2^+## in an excited state with valence configuration ##2\sigma_g^2## ##2\sigma_u^2## ##1\pi_u^2## ##3\sigma_g^1##. Finding all the possible term symbol. Homework Equations Term symbol ##^{2S+1}\Lambda## ##L=0 \rightarrow \Sigma## ##L=1...

am Samuel Owino, a software engineer for the Institute of Biomedical Informatics Research in Eldoret Kenya. I look forward to contributing to the growth of the forum. cheers!

Hi at all, maybe it's a bit trivial. However, the question that i ask myself is ; that relation there is between statistics-probab theory & theoretical physics. What role does it play in theoretical research ? (apart from the probabilistic amplitudes encountered in qm) Thanks for the answers

Hi at all, I've the following question: How the fondamental particles (electrons, protons) are seen as matter waves, what shape and size should be these waves? They are wave-packets?

Homework Statement Is the statement ”Given a two-fermion system, and two orbitals φ labeled by quantum numbers a, b, the two-body wavefunction (1,2 represent the particle variables) $$\psi(1,2) = \phi_a(1) \phi_a(2) - \phi_b(1) \phi_b(2) + \phi_a(1) \phi_b(2) - \phi_b(1) \phi_a(2) $$...

Hi at everyone, why on wiki there is written: " According to modern understanding, the electron is a point particle with a point charge and no spatial extent. Attempts to model the electron as a non-point particle are considered ill-conceived and counter-pedagogic " I don't understand this...

I'm working on an assignment where I'm required to numerically find the energy of a delta-potential's bound state. To do this, we've converted the time-independent schrödinger equation to an eigenvalue problem with E the eigen value, ψ the eigen vector and H a matrix as follows: with ##t =...

Homework Statement The probability for a particle of energy E<<V0 to penetrate a potential barrier of height V0 and width d is approximately \frac{16E}{V_0}exp\left[\frac{-2d\sqrt{2m(V_0-E)}}{\hbar}\right]. An electron moves between two potential barriers of height V0 and 2v0 that are of widths...

Hi at all. I'm wondered is necessary learn well analytical mechanic ( eg learning The Goldstein's book), for understand and study QM ?

Homework Statement [/B]A quantum system has three energy levels, ##-0.12 ~\rm{eV}##, ##-0.20 ~\rm{eV}## and ##-0.44 ~\rm{eV}## respectively. Three electrons are distributed among these three levels. At a temperature of ##1727^o \rm{C}## the system has total energy ##-0.68 ~\rm{eV}##. What is...

Given a wave function $$\Psi(r,\theta,\phi)=f(r)\sin^2(\theta)(2\cos^2(\phi)-1-2i*\sin(\phi)\cos(\phi))$$ we are trying to find what a measurement of angular momentum of a particle in such wave function would yield. Attempts were made using the integral formula for the Expectation Value over a...

Homework Statement How to calculate the probability of finding an 1s electron within 1 picometer cubic region located 50pm from the nucleus. Homework Equations The probability of an 1s electron within a spherical volume of radius 'a' from nucleus can be find using the expression...

I understand that momentum, rest mass and energy can be put on the sides of a right triangle such that the Pythagorean Theorem suggests E^2=p^2+m^2. I understand that the Dirac equation says E=aypy+axpx+azpz+Bm and that when we square both sides the momentum and mass terms square while the cross...

Hello everyone, I started reading the Nielsen and Chuang book on quantum computation and quantum informations. I got stuck by the last question of Problem 2.2. I got the other problems, but i can't see this one. I guess it's not really difficult, but as i am new in this field, some help will be...

I want a QM textbook which introduces detail knowledge of density matrix and trace (i.e. the average), who can recommend one for me? Thank you.

A fictitious system having three degenerate angular momentum states with ##\ell=1## is described by the Hamiltonian \hat H=\alpha (\hat L^2_++\hat L^2_-) where ##\alpha## is some positive constant. How to find the energy eigenvalues of ##\hat H##?

I have encountered a problem that how electric and magnetic fields at perpendicular to each other are produce in electromagnetic radiations?

Hi to all who might respond, Consider the 'peculiar' double-slit setup below. There is a double-slit configuration such that the two slits are never open at the same time. That is: whenever the top slit is open for a certain interval, Ts, the bottom slit is closed for the same interval and vice...

Given a Weyl Hamiltonian, at rest, \begin{align} H = \vec \sigma \cdot \vec{p} \end{align} A Lorentz boost in the x-direction returns \begin{align} H = \vec\sigma\cdot\vec{p} - \gamma\sigma_0 p_x \end{align} The second term gives rise to a tilt in the "light" cone of graphene. My doubts...

Homework Statement I'm reading the book about Statistical Physics from W. Nolting, specifically the chapter about quantum gas. In the case of a classical ideal gas, we can get the state functions with the partition functions of the three ensembles (microcanonical, canonical and grand...

I have taken a couple of graduate level courses in quantum mechanics and I have decided to read Sakurai's Modern Quantum Mechanics from cover to cover, partly because I liked his style and I have heard a lot of people talk highly of it. But I recently realized that the second edition of the same...

What I am interested in doing, is considering the angular momentum eigenstate for a spin ##1## system: ##|J=1, M=1\rangle = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}##, forming the coherent state ##|CS \rangle = \begin{bmatrix} 0.5 \\ -\frac{i}{\sqrt{2}} \\ -0.5...

Hello everyone ! I would like to know if prob. theory is critical to learning Qm !

So I've been reading David Bohm's original paper on the alternative interpretation of quantum mechanics in terms of hidden variables, just out of interest. In the 4th section he presents a complex function ψ in terms of R and S, and then (using the time dependent schrodinger equation, TISE)...

I have encountered this paper "Curie Wiess model of the quantum measurement process". https://arxiv.org/abs/cond-mat/0203460 Another work by the same authors is "Understanding quantum measurement from the solution of dynamical models" https://arxiv.org/abs/1107.2138 I am still evaluating the...

I am reading a proof of why \left[ \hat{L}_x, \hat{L}_y \right ] = i \hbar \hat{L}_z Given a wavefunction \psi, \hat{L}_x, \hat{L}_y \psi = \left( -i\hbar \right)^2 \left( y \frac{\partial}{\partial z} - z \frac {\partial}{\partial y} \right ) \left (z \frac{\partial \psi}{\partial x} -...

Homework Statement Hi, I'm trying to self-study quantum mechanics, with a special interest for the group-theoretical aspect of it. I found in the internet some lecture notes from Professor Woit that I fouund interesting, so I decided to use them as my guide. Unfortunately I'm now stuck at a...

Homework Statement An electron with a total energy of Eo = 4.4 eV is in the potential well shown above. 1) Find the ratio of the wavelength in Region III to the wavelength in Region I. λ III / λI = 1.772) Given that the wave function of the electron vanishes at the left boundary of Region...

In quantum mechanics, the velocity field which governs phase space, takes the form \begin{equation} \boldsymbol{\mathcal{w}}=\begin{pmatrix}\partial_tx\\\partial_tp\end{pmatrix} =\frac{1}{W}\begin{pmatrix}J_x\\J_p\end{pmatrix}...

I'm just starting my journey into physics. I am looking for good quantum mechanics books or articles if anyone has some ideas be sure to let me know.

I always had this doubt,but i guess i never asked someone. What's the main difference between the Classical phase space, and the two dimensional Hilbert Space ?

<Moved from a technical forum, therefore no template> For two non-interacting fermions confined to a 1d box of length L. Construct the antisymmetric wave functions (Slater determinant) and compare ground state energies of two systems, one in the singlet state and the other in the triplet state...

In classical mechanics, the Hamiltonian and the Lagrangian are Legendre transforms of each other. By analogy, in quantum mechanics and quantum field theory, the relationship between the Hamiltonian and the Lagrangian seems to be preserved. Where can I find a derivation of the Lagrangian...

Homework Statement See attached image. The potential in question is, ##-V_0## for ##0<r<a,## and ##0## for ##r\geq a.## Homework Equations $$\sinh(x)=\frac{e^x+e^{-x}}{2}$$ $$\cosh(x)=\frac{e^x-e^{-x}}{2}$$ The Attempt at a Solution I know that the wavefunction for ##r<a## is given by...

I am 16, and I LOVE SCIENCE. I don't really know why, but I do know that I want to be some sort of scientist. I am thinking about doing astronomy or maybe quantum mechanics. I think the two is a fascinating occupation. I also hope to find other science careers that might be interesting. I am...

Homework Statement I'm given that the energy of a particle in a rectangular box is the following: E =\frac{\hbar \pi^2}{2m}(\frac{n_x^2}{L_x^2}+\frac{n_y^2}{L_y^2}+\frac{n_z^2}{L_z^2}) I'm to show that if the length of the box is increased adiabatically and quasistatically from L_x to 8L_x...