Schrodinger equation Definition and 569 Threads

Homework Statement i want to find a pure geometric interpretation of wave function in quantum mechanics Homework Equations i want to solve schrodinger's equation as a second order partial differential equation with a pure mathmatic way to find its geometric analogous The...

The solution of the one dimensional Schrödinger equation for a particle in a one dimensional box is Asin \frac{n \pi x}{a}. But how about if the box is 2D or 3D?

Hi liboff proble 5.28 says time dependent schrodinger equation permits the identity such as E = i\hbar \frac{\partial}{\partial x} (E is operator) But i don't understand E( is operator in this problem) can be thought energy operator Is energy operator only H, Hamiltonian? If E is energy...

Hello. I have a conceptual question about Schrodinger Equation. In the textbook, it says that "Schrodinger Equation contains all the dynamical information that can be known about the wave function", but what exactly is "all dynamical information about the wave function"? Thanks in advance.

Hi everyone, I have been studying Quantum mechanics course for one month and our subject for now is Time-independent Schrödinger Equation. What I couldn't figure out is whether \Psi(x,\,0) = \Psi(x), since \Psi(x,\,0) doesn't contain any time dependence and \Psi(x) as well. Can someone explain...

The intense laser-atom physics becomes hot today. There is a famous interesting phenomenon: High-order harmonic generation (HHG). Lots of works are on the single atom response in the strong field approximation. Some of them obtain the spectrum by solving the Schrödinger equation. Then they say...

Homework Statement Show that the time dependent Schrodinger equation preserves the normalization of the wavefunction 2. The attempt at a solution I don't need help showing this, I'm just not too sure what the question is asking. Do I just show that if a normalized wave-function \psi is a...

Hi there! I'm looking for the solutions of the stationary Schrödinger equation for a potential of the type V = |x| I know that the Airy functions are the solutions to the SE where V \sim x but for the above mentioned potential ... I can't find it -- neither in books nor on the net. Do...

Hello all, How do you prove that, for the normalization of the Schrödinger equation, you can plug in the initial condition of psi(x,t-naught) that will satisfy normalization?

I'm a bit embarrased to ask this (thats why I'm asking here and not asking one of my professors), as a grad student in Physics I've had a good deal of quantum mechanics, but one thing I haven't fully understood yet is the mechanism in the Schrodinger Equation that forces eigenvalue quantization...

Suppose for some specific problem (symmetric potential well) the Schroedinger equation is expected to give certain discrete bound states and corresponding eigenfunctions. Now I am trying to obtain the eigenfunctions by numerically solving the equation and plotting the solutions by randomly...

Suppose I have Schroedinger equation in the form: -u''(x)+V(x)u(x)=Eu(x) The potential is such that as |x| -> Infinity, V(x) reaches a constant positive value. In this case can we have bound state/plane wave solutions for u(x) with E > 0 ?

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}...

When examining the Schrodinger 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 Schrodinger 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...

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 Schrodinger 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 Schrodinger 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 Schrodinger eq. and its general solution...

Considering a step potential of V(x) = o when x<o and V(x) = Vo when x>o so step occurring at origin of x axis. Write down in words the strategy for solving it. Answer: Solve the time-independent schrodinger equation for V=o when x<o and find the solution for the free particle wave function...

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...

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 schrodinger 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 Is this logic correct: begin logic; 1) The Schrodinger equation must hold for all x: 2) The Schrodinger equation contains a second derivative 3) A derivative is only defined on a continuous function. 1, 2, and 3 imply that the first derivative of any...

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 Schrodinger 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 Schrodinger 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 ?

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 Schrodinger equation. Homework Equations Schrodinger'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 Schrodinger 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 Schrodinger 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...

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 independant Schrodinger 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 dependant case?? We haven't gone over that in class so I am not quite...

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

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 Schrodinger'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 Schrodinger Equation and solve for E. Taking my...

Could someone please address this question? How do you algebraically demonstrate the superposition principle revealed by the Schrodinger 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!

By noting that the time dependence of the wave function is governed by the Schrodinger 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...

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

In http://nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html" , he mentions this: I'm trying to get the same result, but I'm stuck. Has anyone done this before?

Complex Schrodinger Equation, references?? hopefully i can explain what i am looking for well enough for somebody to understand. I am interested in finding any references for work that has been done on solving the schrodinger equation in C^n rather than in R^n, as in on the complex plane with...

I have been asked to show that the Schroding equation is equivalent to: i(hbar)d/dt(cn(t))=sum over m (Hnm*cm(t)) where Hnm=integral over all space of (complex conjugate of psin)*Hamiltonian operating on psim psi=sum over n (cn(t)*psin) But i don't know how to even start this question.

I think I copied the wrong notes or something because my notes do not follow. I am trying to find the probability of finding a particle in a box length L in the area \frac{L}{3}-\frac{\partial}{2} to \frac{L}{3}+\frac{\partial}{2} basically we have the following wave funtion...

"You cannot derieve Schrödinger Equation". Bah. We're being told this over and over again. Then the game guy invents operators to extract momentum and energy from wavefunction, then puts them in Newtwon equation! He's saying exactly this: \frac{p^2}{2m} + V = E Should I look amazed when this...