Schrödinger Definition and 591 Threads

If the Hamiltonian is given by H(x,p)=p^2+p then is it Hermitian? I'm guessing it's not, because quantum-mechanically this leads to: H=-h^2 \frac{d^2}{dx^2}-ih\frac{d}{dx} and this operator is not Hermitian (indeed, for the Sturm-Liouville operator O=p(x)\frac{d^2}{dx^2}+k(x)\frac{d}{dx}+q(x)...

hi, today i learned that if the mass in schrodinger equation is not a constant, then schrodinger equation is not valid. Is there any reason why is it so? Also, what is the different of the time dependent mass m(t) and let say a time dependent angular frequency \omega(t) in a harmonic...

Homework Statement b)Use the equations a_{-}|\varphi_0\rangle=0 \implies \left(\left(\frac{k}{2}\right)^{1/2}x-\left(\frac{1}{2k/(2m)^(1/2)}\right)^{1/2}\frac{d}{d x}\right)\varphi_0(x)=0 and a_{+}|\varphi_0\rangle=0 \implies...

Homework Statement the ground state wave function for 1-d SHM oscillator is fixed by the diff. eqn a*phi-0=0using the expression for the lower operator as a differential operator,a-=(K/2)1/2x-h*(\partial)/(2pi*(2m)1/2), to find a solution for this differential equation for phi0(x)...

Hi, is this the time independent schrodinger equation for a simple harmonic oscillator? -\frac{1}{2}\frac{d^{2}\psi}{dx^2}+\frac{1}{2}x^{2}\psi(x)=\epsilon\psi(x) where epsilon is the rescaled energy eigenvalue.

Homework Statement I wonder if someone could help me to arrive at equation 2.56 by performing the substitutions. Please see the attachment Homework Equations Please see the attachment for this part. and also for the attempt of a solution.

Hi everyone, I've recently been bugged by a question I can't seem to find a reasonable answer to. It's about an apparent contradiction between how the wave equation is supposed to evolve in time according to the schrodinger equation and the measurement formalism in QM. Suppose I have any...

Hi I am learning quantum physics in 2nd year i want to know what makes Schrodinger cat quantum? how do we ended up in the Copenhagen interpretation? i.e. probability density function = 0.1; 0<x<10; =0 everywhere else we could say that the particle is simply moving very fast (ignoring...

Homework Statement hey I am vaibhav,16 an 12th grade..just for pastime i tried to solve schrodinger equation in the 1D 2D 3D spaces. i got the 1D solution(not quantum oscillator), i separated in 2D by polar coordinates but there is a problem in the radial equation as for 3D i know that the...

Homework Statement hey I am vaibhav,16 an 12th grade..just as pastime i tried to solve schrodinger equation in the 1D 2D 3D spaces. i got the 1D solution(not quantum oscillator), i separated in 2D by polar coordinates but there is a problem in the radial equation as for 3D i know that the...

Homework Statement Hey guys. I have this problem: http://img32.imageshack.us/img32/1561/78854429.jpg For the first part, I believe that adding those solution is just like adding the two levels of energy they represents and that's way this is not a solution for the equation, I...

Homework Statement For a harmonic oscillator in a state such that a measurement of energy would give either 1/2\hbar\omega or 3/2\hbar\omega with equal probabily. Write the wavefunction solution to the time-dependent Schrodinger equation. 2. The attempt at a solution Given those...

Homework Statement A Particle is described by the normalized wave function psi(x,y,z) = Ae^(-alpha[x^2 + y^2 + z^2]) Where A and alpha are real positive constants a)Determine the probability of finding the particle at a distance between r and r+dr from the origin hint: use the volume of...

Schrodinger equation of a free particle in the rectilinear With the wave function in the laboratory reference already known, relate the wave functions of the initial and new references via phase factors, and represent the time and spatial derivatives of the initial wave function with those...

Homework Statement Show by direct substitution into the time-independent Schrodinger equation that such a particle could be described by the state function Ψ(x) = Ψ_0exp(-ax^2) with a, Ψ_0 constants Homework Equations V(x) = (1/2)kx^2 time independant equation: The Attempt...

i can't seem to understand something very basic about the stationary equation (a "simple" eigenvalue problem): H|Y>=E|Y> H - hamiltonian operator Y - an eigenstate or an eigenfunction of the hamiltonian E - the eigenvalue of the eigenstate as far as i understand, the hamilotian...

Hi, Can somebody point me in the correct direction of learning about Schrodinger Equations in relation to Wave propagation. I came across Schrodinger Equations in some texts but couldn't quite understand some background. Most of the time the author used it from nowhere. Really appreciate if...

Could someone guide me step by step from the free SE to T(t)=e^(iE_n t)/\hbar ? I am not really familiar with PDEs of any kind and I would like slow step by step analysis! I am just confused by the great many ways of getting from there to there I find in books and Internet, so I would like...

Hello, Homework Statement I wondered if someone could help me show / give hints on how to show the (simplified) elastic differential equation (below) is related to the classical Schrodinger equation (in quantum mechanics)? I am a maths undergraduate. 2. Homework Equations - (i had some...

[b]1. State the one dimensional time - INdependant Schrodinger equation for a particle of mass m and total energy E in a potential V(x). For an infinite square potential well V(x)=0 (0<x<l) and V(x) = infinite (all other x) find a general solutionfor the wavefunction of this function of this...

It seems like there should be a discrete-time discrete-space analog to the Schrodinger equation. For example, you can apply the classic explicit finite difference method to the heat equation and get a simple binomial or trinomial tree relationship in a lattice. When I try that with the...

Hi, I am new to this forum. I realized that I was browsing the forums way too much and I said why not register and post some questions that have been lingering in my head: Here is one: In a periodic solid, we almost always neglect the time factor of the Schrodinger equation: e^{-i...

If we solve the Schrodinger Equation for hydrogen atom, we get discrete energy levels that agree with experiment. But no where we need the wave function collapse. So my question is where the wave function come from and why do we need it?

Hello, I would like to ask something about central potentials. When I am working in 3D, I haven´t got any problem solving the schrodinger equation since I use the following change of variables: -\frac{\hbar^{2}}{2m}\nabla^{2}\Psi+V(r)\Psi=E\Psi \Psi=\frac{\chi}{r} With this change of...

i now need to integrate the time-dependent schrodinger equation in 2D the potential is rotationally invariant and so is the initial wave function thus the symmetry of the initial wave function will be preserved in time Instead of a 2D equation, i now only need to integrate a 1d equation...

Homework Statement Show whether the functions psi_I = A cos(kx - wt) psi_II = A sin(kx - wt) are solutions of Schrodinger equation for a free particleHomework Equations Schrodinger equation The Attempt at a Solution For psi_I = A cos(kx - wt), d2psi_I/dx2 = -Ak2psi[/SUB]I[/SUB] dpsi_I/dt =...

Hello again! This time I have another calculus question for you, coming straight out of my study of the free Schrodinger equation, since I am not that experienced with that kind of derivative. It all starts with a given wavefunction (which I think is 2-dimensional,correct me if wrong)...

I was wondering- is it possible to derive an equation of motion for example, the Schrodinger equation from the uncertainty principle (in commutator form)? i.e. Is it possible to derive the Schrodinger equation from the following: \left[\hat{x},\hat{p}\right]=ih I gave it a shot, but of...

the schrodinger equation is sometimes called a wave equation and in my quantum mechanics text's they often show the wave equation comparing it to the schrodinger equation. i don't understand why they do this when it is of the same form as the heat equation, it's not second order in time like the...

Homework Statement Suppose you assume that you have normalised a wave function at t = 0. How do you know that it will stay normalised as time goes on? Show explicitly that the Schrodinger equation has the property that it preserves normalistion over time. Homework Equations From my notes I...

So I've been looking online @ Schrodinger's Equation, but I still can't get a good grasp of what it's all about... All I know so far is that its part of quantum mechanics and that its solutions describe atomic and subatomic systems, electrons and atoms.. <---but what does that actually mean...

Hello, I have problem I wish to solve, and I wonder if anyone already delt with it when solving the schrodinger 2D equation. say E(x,y) is a scalar field function that complies with ( \frac{d}{dx}2+\frac{d}{dy}2 ) *E(x,y)+k(x,y)*E(x,y)=k1*E(x,y) where k(x,y)={k2 for x2+y2<R2 and 0...

Homework Statement Verify that the following are not solutions to the Schrodinger equation for a free particle: (a) \Psi(x,t) = A*Cos(kx-\omega t) (b) \Psi(x,t) = A*Sin(kx-\omega t) Homework Equations Schrodinger equation: \frac{-hbar^2}{2m}\frac{\partial^2\Psi}{\partial x^2} =...

Homework Statement Hello. I'd like to solve this: -\frac{\hbar^2}{2m}\nabla^2 \Psi(r,\theta,\phi) -U(r) \Psi(r,\theta,\phi) = E\Psi(r,\theta,\phi) Homework Equations The Attempt at a Solution I can separate the variables, but that's about it. \frac{1}{R(r)}...

Hi everyone, I'm having an issue trying to make the abstract form of the schrodinger equation: i\hbar\frac{\partial}{\partial t}\left|\psi\right\rangle = H\left|\psi\right\rangle be consistent with the form that operates on wavefunctions in the position representation...

Assume the potential in question is V = \left\{ \begin{matrix} \infty, \qquad x<0 \\ -V_0, \qquad 0\leq x \leq a \\ 0, \qquad x>a \end{matrix} \right. where V_0 is positive. if we need to find the bound state, we consider the energy is less than the potential. But the...

Homework Statement Please see attached image . Homework Equations Schrödinger Equation The Attempt at a Solution For part a ) |\psi|^{2} = A For Part b) V(x) = 0 For Part c) Just need a hint

Homework Statement Please see attached image . Homework Equations Schrödinger Equation The Attempt at a Solution For part a ) |\psi|^{2} = A For Part b) V(x) = 0 For Part c) Just need a hint

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...

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 ?

I wish to graph a couple of the waveforms of a harmonic oscillator. I have consulted several resources and have found two that I like but the final equation differs even though they are both labeled normalized harmonic oscillator wavefunction. The first reference explains how the harmonic...

The problem is the picture below. The thing I don't understand, since I also have the solution, is the fact that the "radial wavefunction is normalized to 1". And all the constants before it aswell. Why can't I move out the constants in front of the integral, normalize it and then get a...