Schrödinger Definition and 591 Threads

Homework Statement Two identical particles, each of mass m, move in one dimension in the potential $$V = \frac{1}{2}A(x_1^2+x_2^2)+ \frac{1}{2}B(x_1-x_2)^2$$ where A and B are positive constants and ##x_1## and ##x_2## denote the positions of the particles. a) Show that the Schrodinger equation...

Hi, I am wondering why every general solution to Schrodinger equation can be built from separable solutions. In other words, I don't follow that why every solution to Schrodinger equation can be written as $$\Psi(x,t) = \sum c_n\Psi_n(x,t)=\sum c_n\psi_n(x)\phi_n(t)$$ I know that the right hand...

The problem looks very simple. We have a time-dependent Hamiltonian: $$H(t) = B(t)H_0$$, where ##B(t)## is a numerical function, and matrix ##H_0## is time-indpendent. Let us consider: $$B(t) = \begin{cases} 1,&\text{for $0\leq t\leq t_0$}\\ A,&\text{for $t>t_0$.} \end{cases}$$ Also, let us...

Suppose I want to solve the Schrödinger equation numerically for some potential V(x). The easiest way to do so, is to discretize it on a grid of finite length, and apply a finite difference scheme to approximate the second order derivative. Doing so yields an eigenvalue equation on matrix form...

Homework Statement This is a (long) multi-part question working through the various stages of solving the radial Schrodinger equation and as such it would be impractical to type it all out here but I will upload the pdf (https://drive.google.com/open?id=0BwiADXXgAYUHOTNrZm16NHlibUU) of the...

Suppose I want to solve the time-independent Schrödinger equation (ħ2/2m ∂2/∂x2 + V)ψ = Eψ using a numerical approach. I then discretize the equation on a lattice of N points such that x=(x1,x2,...,xN) etc. Finally I approximate the second order derivative with the well known central difference...

Schrodinger Equation is the very first step when we start learning QM. However, I never learned about the physical meaning of it. I have read a number of articles and discussion online. Regarding the ones I understand, there are generally two points of view. 1. Fundamental physical laws are not...

So I have previously learned how to discretize the Schrödinger equation on the form: (p^2/2m + V)ψ = Eψ , where the second order derivative is approximated as: (ψi+1+ψi-1-2ψi)/2Δx Such that the whole equation can be translated into a matrix eigenvalue-equation. The problem is that I am now...

Hi, I am a student in the Netherlands, currently 17 years old and at the end of my 'middelbare school', meaning that next year I'll be a bachelor student at a university. I am doing an extended essay/research thing that is custom you do in your last year, with a friend of mine. We picked the...

Once again, I came across the notion (in a lay physics book by an academic) that two mutually exclusive states simultaneously exist until observed (based on the Schrödinger living/dead cat thought experiment), which, on its face, seems to me to belong to theology and not to science. That both...

Hi folks, I just want to check I understand correctly the Schrodinger equation for two electrons. https://en.wikipedia.org/wiki/Schrödinger_equation#Time-independent_equation With control F you can find "two electrons atoms or ions" section. Let's assume the wave function = x1 2+ x22 and...

Homework Statement Lets say f(x) is a solution to TISE. If it is, why is its complex conjugate f*(x) a solution too? Homework Equations TISE = time independent Schrodinger equation The Attempt at a Solution ?

The Dirac equation is the more generalized form of the Schrodinger equation and accounts for relativistic effects of particle motion (say an electron) by using a second order derivative for the energy operator. If you have an electron that is moving slowly relative to the speed of light, then...

Why doesn't The Feynman Lectures consider the possibility of negative ##\alpha## when it says that ##e^{+2\alpha\rho}## is a rapidly increasing exponential (just below http://feynmanlectures.caltech.edu/III_19.html#mjx-eqn-EqIII1923) ?

On the Schrodinger cat, can I simply say, outside the box,the state is in superposition,but inside the box, the state is not. Besides, the experiment is so simple to do, how come no body ever did it ?. Just put an animal you hate or even an inset, and observe the expected (50% -50%) result...

I know there's a similar post, but i didn't understand it. Why the derivative respect to t in terms of the complex conjugate of ψ is: instead of being the original S.E in terms of ψ* or the equation in terms of ψ with the signs swapped

I decided to perform a little thought experiment -- without the mathematics. Assume we have two Schrodingers' Cats. After a while, they will be in a superposition of being alive and dead at the same time. Now assume that they are entangled, and we open the boxes at the exact same time. Cases...

Given 1A.1 and 1A.2, I have been trying to apply the Schrödinger equation to reproduce 1A.3 and 1A.4 but have been struggling a bit. I was under the assumption that by applying ##\hat{W} \rvert {\psi} \rangle= i\hbar \frac {d}{dt} \rvert{\psi} \rangle## and then taking ##\langle{k'} \lvert...

Hello everyone, I have this weirdo potential for homework \begin{equation} U(x) = \frac{U_1}{ \left( 1+e^{x/a}\right)^2 } - \frac{U_2}{ \left( 1+e^{x/a}\right)} \end{equation} where U1,U2 and "a" are positive and I need to find the energies for the bound states and also the wave functions...

I have read that the Schrodinger Uncertainty Principle is an extension of Heisenberg's. So, why don't we use the Schrodinger Uncertainty Principle instead of Heisenberg's? Thanks!

Homework Statement I have an attachment Homework Equations Schrödinger equation The Attempt at a Solution The issues I am having is how to start this one. This is not a infinite square well but a semi-infinite square well. I know that energy= K^2= 2mE/h^2 Where h is planks constant 6.626 X...

The solution to the One-Dimensional Time-Independent Schrödinger equation for an electric potential field of constant value is an exponential function, and its energy eigenvalue can have any value, it is not quantised. Are there any other potential field functions whereby the energy of the...

I'm trying to integrate the Schrodinger equation ##i\hbar \frac{d}{dt} |\psi(t)\rangle = H |\psi(t)\rangle## with the initial condition ##|\psi(t_{0})\rangle=|\psi_{0}\rangle## to show that ##|\psi(t)\rangle = \exp(\frac{t-t_{0}}{i\hbar}H)|\psi_{0}\rangle##. I know how to plug in the solution...

According to my textbook the nonlinear Schrödinger equation: $$\frac{\partial A(z,T)}{\partial z} = -i \frac{\beta_2}{2} \frac{\partial^2A}{\partial T^2} + i \gamma |A|^2 A \ \ (1)$$ can be cast in the form $$\frac{\partial U(z,\tau)}{\partial z} = -i \frac{sign \beta_2}{2} \frac{1}{L_D}...

If we were to assume that the electron moves around the proton with radius a, the Schrodinger equation becomes: ##\frac{1}{a^2}\frac{d^2\psi}{d\phi^2} + \frac{2m}{\hbar^2}|E|\psi = 0## The question in my textbook asks me to solve the above equation to obtain values of energy and angular...

Homework Statement Trying to use change of variables to simplify the schrodinger equation. I'm clearly going wrong somewhere, but can't see where. Homework Equations [/B] Radial Schrodinger: -((hbar)2)/2M * [(1/r)(rψ)'' - l(l+1)/(r^2) ψ] - α(hbar)c/r ψ = Eψ The Attempt at a SolutionWe're...

Is the solution of the time-independent schrodinger equation always a stationary state? Can it be non-stationary?

This has come up in a number of threads, so I made this thread to talk about it. I think that an interpretation of this in the Schrödinger picture should be possible at least in the style of Feynman. This would go something like this. ##\begin{eqnarray*} \langle A(s)A(t)\rangle_\psi &=&...

Just like it says, are all solutions of the 1D time independent Schrodinger equation, by default, energy eigenstates? I'm having a hard time imagining how solutions, with these conditions, that aren't energy eigenstates could exist if they have to satisfy the relation E \psi(x)=\hat{H}\psi(x)

Homework Statement Homework Equations \begin{align} \begin{split} \psi(x, t) = e^{(ikx- i \omega t)} \\ V(x) = 0 \end{split} \end{align} The Attempt at a Solution For a free particle, the Schrödinger equation can be put in the form of ##\psi(x, t) = e^{(ikx- i \omega t)}##...

I am reading a lot about how to calculate band bending from solving the Schrödinger equation and Poisson equation self-consistently. To recap some of the central ideas are: We look at the conduction band of some semiconductor. If we assume that the electrons are free electrons with some...

Hello everybody, My question is about variable separation applied in the solution of general time-independent Schrodinger equation, expressed with spherical coordinates as: \hat{H} \psi (r,\theta,\phi) = E \psi (r,\theta,\phi) Is it always possible (theoretically) to seek a solution such as...

Homework Statement There is a stream of electrons with energy E, incident from x = -∞ on a potential step such that V(x) = ##V_{0}## for x<0 and 0 for x>0. E>##V_{0}##>0. Write the T.I.S.E for x<0 and x>0 and find the general solution for both. Homework EquationsThe Attempt at a Solution My...

I think that all is in the title. If the amplitude ##\phi## obeys a Schrodinger equation, what is the law for ##p = \phi^* \phi##?

When I was young I read Schrodinger's memoirs. I can't find a book, but I remember he described an interesting conversation with Max Planck about what to do during the political catastrophe. The conversation was in 1940, and Schrodinger was asking Planck's opinion on what to do - to immigrate...

I found this question here but i do not understand the answer. One equation is from classical physics and the other from quantum physics. Is there another way to go from classical to quantics than the analytical extension?

Homework Statement (See attached photo) Homework EquationsThe Attempt at a Solution I Have no clue where to start for b), i need major help! For a I said that you can argue since the potential is symetric along the x-axis that this operator will go to 0. However I don't know where to start for...

Homework Statement (See attached picture) Homework EquationsThe Attempt at a Solution I'm not even sure where to start :( I'm assuming that i have to find a wave function outside and inside the well and meet certain boundary conditions, but I am confused. Please help.

Homework Statement Verify that a plane wave ψ(x) = Ae-ikx is a solution to the time independent Schrodinger equation for a free particle in one dimension. Can it be normalised? Why?[/B]Homework EquationsThe Attempt at a Solution My lecturer's notes are all over the place, which is frustrating...

Homework Statement Let |v(t)> ∈ℂ^2 by the time-evolving state of a qubit. If |v(0)> =\begin{pmatrix} 0 \\ 1 \end{pmatrix} , and the Hamiltonian of the system is H = \begin{pmatrix} 0 & -iλ \\ iλ & 0 \end{pmatrix} (where λ∈ℝ) what is |v(t)>?Homework Equations Time dependent schrodinger...

I have just recently started learning about quantum contextuality and can only seem to find examples where contextuality is need to explain measurements of spin. So I am curious as to whether quantum contextuality only applies to measurements of spin? Also, If someone could clarify where the...

Homework Statement Consider the one-dimensional Schrodinger equation for the step potential, that is for U(x) = 0 for x<0, and for , . Consider a particle with mass m and energy E < U. Assume the particle is initially at x<0. a) Calculate the penetration depth Δx at which the probability...

The following extract is taken from Appendix A of the following paper: http://arxiv.org/abs/0810.0713.Any solution of the Schrodinger equation with rotational invariance around the ##z##-axis can be expanded as ##\psi_{k}=\Sigma_{l}A_{l}P_{l}(cos \theta)R_{kl}(r)##, where ##R_{kl}(r)## are the...

Homework Statement Consider the time-dependent Schrodinger equation for a free particle in two spatial dimensions Using the method of separation of variables, determine the wave function ψ(x,y,t) Homework EquationsThe Attempt at a Solution Not sure how to do the separation here since it is...

I have a question about photons and the Schrödinger equation. Photons behave like particles but also as waves. I understand that this can be described by the Schrödinger equation as a photon having a certain probability to be somewhere. If I understand this correctly, I take it that there are...

In Grifftiths Intro to Quantum 2nd edition, page 51, he is re-expressing the Schrodinger equation for a harmonic oscillator in terms of a unit-less quantity \xi \equiv \sqrt{\frac{m\omega}{\hbar}}x So Griffiths takes the Schrodinger equation in equation [2.70] -\frac{\hbar^2}{2m}...

I am simulating electrons inside a cylindrical well like the one shown on the first figure. My current work has been on solving the Schrodinger equation numerically for the above potential and then finding corrections to the solution such that it is consistent with Poissons equation. To do so...

1. Homework Statement p: momentum x: position t: time h_bar: Planck's constant Ψ: wave function Homework Equations The Attempt at a Solution I've posted a link to pictures. http://imgur.com/a/TKvUu I'm not vera good at using LaTex yet :( So I've shown that the wave equation satisfied the...

I am right now working on a script that solves the Schrodinger equation numerically for arbitrary potentials using the finite difference method. The idea is that I diagonalize the Hamiltonian with elements: H(i,i+1)=1/dx^2 * constants H(i,i-1)=1/dx^2 * constants H(i,i) = -2/dx^2 * constants and...