Schrodinger equation Definition and 549 Threads

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...

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 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...

At this link: http://www.geocities.com/ptep_online/PP-04-07.PDF is a recent paper by Carlos Castro on a new nonlinear Schrodinger equation--for those that work in this area.

Schrödinger equation: P(r)>1 ? I have the solution of the Schrödinger equation for the ground state of the hydrogen electron. The solution ist: u100(r)=sqrt(1/(pi*a^3))*exp(-r/a) If I want to calculate some probabilty values I do this with: P(r)=4*pi*r^2*|u100|^2 If I set r=10^-13 I...

I'm given the value of a normalized wave function at t=0 (see attachment) and I'm asked to find the wave function at some time t. I have no idea where to even begin, the book has zero examples of anything and I'm just stuck :confused:

May be this is a silly question, but if one converts the nonrelativistic Schrödinger equation for a free particle to an uniformly accelerated frame, is the result the same as the Schrödinger equation for a particle within a gravitational potential? I was trying some simple calculations but did...

what is the physical significance of each of the terms in the 1-D time indipendant schrodinger equation?

Hi, I am looking for a book which explains the solving methods for 3d schrodinger equation. Can you help me? Roitan

Hi, I am looing for a book that explains the solving methods for 3D schrodinger equation. Can anybody help me? Sanam

If H1=P^2/2m+V1(x), H2=P^2/2m+V2(x), H=P^2/2m+V1(x)+V2(x) and H1 f1_i(x)=E1_i*f1_i(x), H2 f2_j(x)=E2_j*f2_j(x), H f_k(x)=E_k*f_k(x) Is there any relation between f1_i(x),f2_j(x),f_k(x)?Can we express f_k(x) in terms of f1_i(x) and f2_j(x)?

I am trying to find the Schrodinger's equation for the one-dimensional motion of an electron, not acted upon by any forces. So.. should I begin using the time independent form of the Schrodinger's equation? What should I arrive at? Should I let my V(x) = 0? Also, how do I show that...

Ok, I know that the 1D time-independent Schrodinger equation is -\frac {\hbar^2} {2m} \frac {d^2 \psi(x)} {dx^2} + V(x) \psi(x) = E \psi(x). Why is it that you can mix potentials and energies in the same equation? For example, if you're saying that V(x) has a constant value, say, V(x) = V_{0}...

can you explain this statement "if psi is a solution of a schrodinger equation, then so is kpsi, where k is any constant". why is that multplying psi by a constant does not its value?

Hi, I have a problem. I want to show that \frac{d}{dt} \int_{-\infty}^{\infty} \psi_1^{*}\psi_2 dx = 0 for any two (normalizable) solutions to the Schrödinger equation. I have tried rearranging the Schrödinger equation to yield expressions for \psi_1^{*} and \psi_2 like this...

:confused: Newton's equation (F=ma) could derive from Lagrangian, My question is, could we derive the schrodinger equation from the more fundemantal principle in Physics...

In the very first pages of "Quantum Mechanics" by Landau & Lifchitz, the measurement process is described as an interaction between a quantum system and a "classical" system. I like this interpretation since any further evolution of the quantum system is anyway entangled with the "classical"...

One solution to the time-independent Schrödinger equation for a free particle (moving in 1 dimension) is: \psi(x) = Ae^{ikx} This has a definite momentum p = h-bar*k, but it can't be normalized since: \int_{-\infty}^{\infty}\lvert\psi(x)\rvert^2dx = \int_{-\infty}^{\infty}|A|^2dx =...

Ok, so suppose there is a free particle of mass m that moves in a one-dimensional space in the interval 0<=x, with energy E. There is a rigid wall at x=0. Write down a time independent wave function G(x) which satisfies these conditions, in terms of x and k, where k is the wave vector of motion...

one-dimensional Schrodinger's Equation Hi ! I wonder how to solve one-dimensional Schrodinger's Equation : \frac{d^2 \psi (x)}{dx^2}\ = \ -(\frac{2 \pi}{\lambda})^2 \ * \ \psi (x) I've to obtain \psi (x) , when -(\frac{2 \pi}{\lambda})^2 is known Can you solve it as an example...

I am looking for a detailed step by step derivation of the Schrodinger Eqn. where one will obtain the general solutions for R, Thetha, and Phi for the hydrogen atom. If someone could direct me to a reference of these derivations explained step by step it would be of great help. [b(] --Wall...

I'm dong a presentation and I'm trying to explain how to use the Schrodinger Equation to find the wave function of a particle. And I have never done that before...I have a basic idea, but to be more accurate, I need you guys' help. Note that this is for a 7th grade class presentation (so if...