Schrödinger Definition and 591 Threads

A massless particle situated in a 1D infinite square well with momentum only in the direction of quantum confinement (the x direction): E_t \psi (x) = \hbar \omega \psi (x) = i \hbar \frac{\partial}{\partial t} \psi (x) p(x) \psi(x) = \hbar k_x \psi (x) = -i \hbar \frac{\partial}{\partial x}...

I have looked at several derivations of the Schrödinger equation but the one I like the best is from Piravonu Mathews and K. Venkatesan in their book ‘A Textbook of Quantum Mechanics’. I follow their logic and algebra up until the last step were they arrive at the Schrödinger equation for one...

Why did Schrödinger call his equation eigenvalue problem? We can solve Schrödinger equation since it's just differential equation with complex number

I have a simple question but can't find the answer: What happens in the Potential Step (the Schrödinger Equation aplication) case when E = V0 ? I only seem to find the cases when E>V0 or E<V0. Thanks in advance!

What is the relationship between the "matter waves" described by de Broglie, the probability amplitude function and Schrödinger's wave equation? I've read the following: "The wavelengths postulated by de Broglie to be associated with the motions of particles are in reality the wavelengths...

When examining the Schrödinger equation for a particle in a square well there is a lower case “i” that shows up in the equations that never gets defined. I have checked several sources and its usage is somewhat uniform and yet not defined. Can someone define the “i” ? One source I am...

Homework Statement Stationary Schrödinger equation for a particle moving in a potential well has two solutions psi1(x)=e^-ax^2 with energy E1 and psi2(x)xe^-ax^2 with energy E2 At t=o, the particle is in the state psi(x)=psi1(x)+psi2(x) Calculate the probability distribution as a...

Homework Statement I'm just wondering how you get the energy levels from the Schrödinger equation. I've got the equation in the form H(psi) = E(psi) with all the H expanded out, I just don't know how to calculate the energy levels from it. Its probably something I did once know how to do, but...

How can I write the Schrödinger equation for the harm. oscillator in momentum space and then solve it? Thank you, in advance:)

In the potential well example we are considering the potential in the well to be zero and infinite outside the boundary, does this mean that the electron can move freely such that there is no opposition or restoring energy acting on it. And also the probability of finding the electron is...

Why momentum is replaced by momentum operator in Schrödinger equation ?

I hope I'm not offending anyone here by posting a request for some help here. We are in need of a knowledgeable physicist who can interpret an anomoly in a Schrödinger equation graph. This is for an online alternate reality game ("ARG") called Find the Lost Ring. The graph can be found here...

Homework Statement A particle of mass m and energy E, where E >V1 >V2 travels to the right in a potential defined as V(x) = V1 for - b < x < 0 V(x) = 0 for 0 < x < a V(x) = V2 for a < x < b (a) Write down the time-independent Schrödinger eq. and its general solution...

I have a project to work on that's due by mid March. I would need to write a computer program, to show how a wave packet reflect off a barrier? How much of the wave reflects off a wall of finite height and thickness, and how much tunnels through? I remember doing something similar in my...

Hi I am new to quantum physics and i have been asked to find the dimensionless Schrödinger EQ for a wave function it says sub in t = (2/ohm)*tor and x = sqrt(h-bar/m*ohm)z now do i just put in these values and diffreinchiate threw ? or is it more complex ? thank you for your time Ross Taylor

[SOLVED] angular equation (Schrödinger) Hi, I don't now how to pass from the form1 to Associated legendre fuction (form2) in the attache file .doc Someone can help me? Thanks :)

[SOLVED] Calculate time evolution of Schrödinger wave equation Homework Statement At time t=0 particle is in state: \psi\left(x\right)=\sqrt{2}A\phi_{1}(x)+\frac{A}{\sqrt{2}}\phi_{2}(x)+A\phi_{3}(x) where \phi_{n}(x) are eigenfunctions of 1-D infinite potential well. a) Normalize...

Neither in Sam Treiman's http://books.google.de/books?id=e7fmufgvE-kC" I was able to find the Schrödinger equation for a photon, i.e. a particle without rest mass. The Schrödinger equation straight from Treiman's book (typos are mine, if any) -\frac{\hbar^2}{2m}\Delta\Psi + V\Psi =...

I have a problem on the basis of quantum mechanics and it's so simple that I'm almost too afraid to ask. Anyway: 1.) Schrödingers differential equation is used for time indepent and time depent problems. The solution is a wave function or the linear combination of the resulting wave...

Homework Statement The wave function of a particle satisfies the time-independent Schrödinger equation. If the potential is symmetric and has the form V(x) = \inf |x|>1.0 V(x) = \frac{\hbar^2V_0}{2m} |x|<0.2 V(x) = 0 Elsewhere Using the shooting method, I need to find the...

Homework Statement Im doing an A-level project on the Schrödinger equation and am unsure on the mathematics used to obtain the following results: The Schrödinger for a particle in no potential field (=0) has the solution: psi(x)=e^ikx. i is defined below, I haven't really a clue as to...

Homework Statement Show that \Psi(x,t) = Ae^{i(kx-\omega t)} is a solution to the time-dependent Schrödinger equation for a free particle [ U(x) = U_0 = constant ] but that \Psi(x,t) = Acos(kx-\omega t) and \Psi(x,t) = Asin(kx-\omega t) are not. Homework Equations - \frac{h^2}{4\pi...

Is it possible, in theory, to describe a macroscopic object with the Schrödinger equation (its location for example)?

I have read the following claim (where is not important): ...the Schrödinger equation provides no rational basis for the phenomenon of spin, the Pauli Exclusion Principle, or Hund's Rule... Is such a claim true ? If so, what does it matter ?

For the well shown below (Attachment or Link belew) solve the time independent one dimensional Schrödinger equation for energies less than V0. You may (and should) leave your answer in terms of a single transcendental equation for the allowed wave numbers. \frac{-\hbar^2}{2m} ...

My own question, carried to a new thread as not to derail another:

Homework Statement Consider a particle of charge e and mass m in crossed E and B fields, given by E = (0,0, E), B = (0,B, 0), r = (x, y, z). Write the Schrödinger equation. Homework Equations Schrödinger's equation: \left[ -\frac{\hbar^{2}}{2m} \nabla^{2} + V(r,t) \right] \Psi(r,t)...

Hi all. What do it mean by "slow variables" in NLS? I am reading a derivation of the NLS in the context of hydrodynamics, by R.S.John in his book "A modern introduction to the Mathematical Theory of Water Waves". In the book, slow variables are zeta = epsilon * (x-ct) and T = epsilon * t...

For a free particle, show that the time-independent Schrödinger equation can be written in dimensionless form as d^2\psi(z)/dz^2 = -\psi(z) . I do not see how you would get rid of the m (with units mass) in front of the del in the SE (or the other constants for that matter)...

I am somewhat confused about how general the solution \psi_E(x) = Aexp(ikx)+Bexp(-ikx) is? Can someone complete one or both of these sentences: \psi_E(x) = Aexp(ikx)+Bexp(-ikx) is the solution to all equations of the form ... or \psi_E(x) = Aexp(ikx)+Bexp(-ikx) is a...

Hello everyone! I am a new member and please sorry for some question that perhaps were discussed here before. But really I need your help. I am searching for methods of solving 3 dimensional Schrödinger equation. Till now in internet I coulnd't find any solution. All the papers and articles are...

I'm currently reading Griffith's book on time independent Schroedinger's equation about delta functions. However, I complete dislike how the book deals with the delta distribution. firstly, the book discusses how to solve: -\frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2}-\alpha\delta\psi=E\psi for...

Sorry, I'm new, can someone provide a simplified (i.e. dumbed-down) explanation of the Schrödinger equation? i understand some of the basics of quantum mechanics, and i find this thread fascinating. at the base level, this seemed like a fairly straightforward question, but it seems there are...

Hello! I'm trying to solve some old exam exercises to prepare for my qm exam next week. Now I got a question I don't have any idea how to solve it. I hope somebody can help me: "The radial Schrödinger equation in the case of a 3D spherical symmetric potential V(r) can be written in the...

Hi, I have been wondering why we can consider d(phi)/dt when we are in Schrödinger picture (phi is just the usual scalar field here). Isn't this 0 as operators do not depend on time in this picture? However then how does it make sense to talk about the conjugate momentum in this picture which...

I've suddenly run into a problem. This has probably arisen from the fact that I've yet to have (and may never have) formal teaching on the relativistic generalisation of QM. I see the Schrödinger equation proper as \hat{H}| \psi (t) \rangle = i\hbar \frac{d}{dt} | \psi (t) \rangle Is this...

Homework Statement A particle of mass m moves in three dimensions in a potential energy field V(r) = -V0 r< R 0 if r> R where r is the distance from the origin. Its eigenfunctions psi(r) are governed by \frac{\hbar^2}{2m} \nabla^2 \psi + V(r) \psi = E \psi ALL in spherical coords...

Note that this is not homework... I am just curious The time independent Schrödinger equation can be written as \hat{H} \psi = E\psi IS there ever a time taht the above equation is not true?? what about the time independent case?? We haven't gone over that in class so I am not...

If using spherical coordinates (r, theta, phi) , what is the meaning of the canonical momentum of theta, phi? What are their definitions and mathematical form? In solving the Hydrogen problem, one has not take into consideration P_theta and P_phi at all. Quantum River

A couple of things first - Whats an eigenfunction? Whats an eigenvalue? I've been doing a course on quantum mechanics for nearly 2 months and whilst these words have popped up in both notes and lectures no-one has actually bothered to explain what they are or what they mean! Next thing. Can...

I'm looking to solve schrodingers equation for the bound energy state energy eigenfunctions, for a particle in a 1-D potential well (E<Vo), where; V(x)= (inf, x<0) (0, 0<x<a) (Vo, x>a)so we know when x>a our function is going to be a negative exp, and between 0 and a the function is...

So, here's the question: \psi(x) = A*(\frac{x}{x_{0}})^n*e^(\frac{-x}{x_{0}}) Where A, n, and X0 are constants. Using Schrödinger's equation, find the potential U(x) and energy E such that the given wave function is an eigenfunction (we can assume that at x = infinity there is 0...

I have a time dependent wavefunction for inside a delta function potential well: V(x) = -a delta(x). It reads Psi(x,t) = (sqrt(m*a)/hbar) * exp(-m*a*abs(x)/hbar^2) * exp(-iEt/hbar) I'm supposed to stick this back into the time dependent Schrödinger Equation and solve for E. Taking my...

Could someone please address this question? How do you algebraically demonstrate the superposition principle revealed by the Schrödinger equation (ie. If Psi1(x,t) and Psi2(x,t) are both solutions then Psi(x,t)= Psi1(x,t)+Psi2(x,t) is also a solution.)?

HELP! I need to find the energy emitted by a photon if an electron is confined in an infinitely deep well. Can someone tell me what the hell to do please?! I'm desperate! Thanks!

I have just read that Schrödinger had wrote six research papers ( in 1926) in which he presented the complete mathematical foundation of nonrelativistic quantum mechanics . Also read that De Broglie supported his proposal (the duality) by a proof derived from relativity theory . Are these...

Here is an objective question: The first full presentation of the behavior of electron in hydrogen atom by using wave mechanics is by: Louis de Broglie or Schrödinger? As far as I know, Schrödinger is famous for his wave equation. Meanwhile, de Broglie is known for the equation lambda= h/mv.

By noting that the time dependence of the wave function is governed by the Schrödinger equation show that \frac{d(\Psi^* x \Psi)}{dt} = \frac{i \hbar}{2m} \left[x\Psi^* \frac{d^2\Psi}{dx^2} - x \Psi \frac{d^2 \Psi^*}{dx^2} \right] not sure where to start on this one actually... do i start...

Hi all, I'm trying to solve the 1D Schrödinger equation for an arbritary potential, to calculate Franck Condon factors for absorption and emmision spectra. I can do this using iterative techniques (e.g. the Numerov method), but I can't seem to get it to work by discretrizing the hamiltonian...

I read article http://www.oup.co.uk/pdf/0-19-850687-2.pdf There is described Schrödinger equation in gravitational field (1.10) and COW experiment. But once I found article, where it is shown that this Schrödinger equation is in direct contradiction with principle of equivalence. Can...