Schrödinger Definition and 611 Threads

I would like to discuss the Schrödinger equation in order to get some insight. The equation, as I understand it, is essentially an expression of the conservation of energy. What it says is that ∆Total Energy= ∆ Kinetic Energy + ∆ Potential Energy. In Schrödinger's day, there were various...

As part of my project I was asked to use the finite difference method to solve Schrodinger equation. I see how you can turn it into a matrix equation, but I don't know how to solve it if the energy eigenvalues are unknown. Are there any recommended methods I can use to determine those...

Hello, I am trying to find the solution of Schrödinger equation on matlab. However, when I apply boundary conditions, MATLAB only gives me the solution with both coefficients 0. I want to find the solution : Asin(n*pi*x/L) You can see my code below. Could you please tell me where is my mistake...

In the Schrodinger picture, the operators don't change with the time, but the states do. So, what happen if my hamiltonian depend on time? Should I use the others pictures in these cases?

I apologize for the bad formatting: To start off, I'm trying to use the Schrodinger Equation in the form: (ħ/2m) d^2Ψ(x,t)/dx^2+V(x,t)Ψ(x,t)=EΨ(x,t) I couldn't remember if I need to also take the partial derivative with respect to T as well, but I started off with just X. I plugged in my...

Has anyone formulated a general solution to the time-independent Schrödinger equation in terms of the potential function V(r), and if so, what is it? For any type of V(r). So, instead of a differential equation, a direct relationship between the wavefunction and the potential.

Symmetry transformations are changes in our point of view that preserve the possible outcomes of experiment: $$\Psi \rightarrow U(\Lambda) \Psi$$ In the Heisenberg picture, observables in a fixed reference frame evolve according to: $$P(t) = U^\dagger (t)PU(t)$$ while in the Schrodinger...

This paper was recently published in the Monthly Notices of the Royal Astronomical Society. Batygin 2018, Schrödinger Evolution of Self-Gravitating Disks I am posting this in here, but I am actually more interested in the implications of looking at this the other way around: namely, from a...

I had a question about Schrodinger's cat that extends to the universe. First, I'm sure everyone knows the Schrodinger's cat set up so I won't repeat it. I will just ask, how can the cat be dead or alive prior to measurement? This measurement would be either atoms in the radioactive substance...

I've been studying the 1D schrodinger equation, and getting a feel for solutions in the harmonic oscillator, or potentials of inverse radius (atomic/hydrogen), and many versions of stair-step/ square potentials (square wells.) But, I've noticed that there are very few exact 1D potentials in the...

Hello everyone, For weeks I have been struggling with this quantum mechanics homework involving writing a code to determine the energy spectrum and eigenvalues for the stationary Schrodinger equation for the harmonic oscillator. I can't find any resources anywhere. If anyone could help me get...

Hi everybody, For solving the time dependent Schrödinger equation ##H|\psi(t) \rangle = i\hbar \frac{\partial}{\partial t}|\psi (t)\rangle##, I read in quantum mechanics books the assumption about the solution ##|\psi(t) \rangle## which is made of a linear combination of a complete set of the...

I've seen a proof that the path integral formulation of quantum mechanics is equivalent to solving Schrodinger's equation. However, it appears to me that the proof actually depended on the Hamiltonian having a particular form. I'm wondering how general is the equivalence. Let me sketch a...

Homework Statement For a wavefunction ##\psi##, the variance of the Hamiltonian operator ##\hat{H}## is defined as: $$\sigma^2 = \big \langle \psi \mid (\hat{H} - \langle\hat{H}\rangle)^2 \psi \big\rangle$$ I want to prove that if ##\sigma^2 = 0##, then ##\psi## is a solution to the...

I'm reading through a couple of books (Lahiri & Pal's "A First Book of Quantum Field Theory" and Greiner & Reinhardt's "Field Quantization" and have come to the derivation of the evolution operator which leads to the S-matrix. In both books, the derivation starts with the Schrodinger equation in...

It seems to me that so far in quantum mechanics, because we have yet to establish probability patterns for, say, what the spin of a photon is, we have made it some mystical thing that we can only know by measuring it. I don't really buy that; is the result of a lottery impossible to know until...

Homework Statement [/B] The Hamiltonian and wavefunction for the ground state of the hydrogen atom H(1s1) are given, in atomic units, as ## \hat {H} = - \frac{1}{2} \nabla^2 - \frac {1}{r} ## and ## \phi(1s) = \sqrt {\frac {1}{\pi }} e^{-r} ## . Using the radial portion of the Laplacian in the...

Suppose we have a particle of mass ##m## moving freely in the xy-plane, except for being constrained by hard walls to have ##-L/2 < y < L/2##. Now, the energy eigenstates would be something like ##\psi (x,y) = C \psi_x (x) \psi_y (y) = C e^{-ikx}\cos\left(\frac{n\pi y}{L}\right) ##, where...

Hello all, you may already know that Q.M. is a linear theory however there is something called nonlinear Sch. eq. for example Gross-Pitaevskii equation. How can such a thing exist considering that Q.M. is a strictly linear theory. Cheers.

When reading a textbook I came across some reasoning about Schrödinger Equation. It started with the wave function $$\nabla^2\psi=k^2\psi$$ I am a bit lost at this point. Where does the right side of the equation come from? What should I review to fix that part of my knowledge?

I recently found this article about the dynamics of the wave function. It has some good simple illustrations and I found it valuable. But the author has a question himself, about understanding the Schrodinger equation. I wonder if anybody here could fill in the missing piece. The relevant part...

The time-dependent Schrodinger equation is given by: ##-\frac{\hslash^{2}}{2m}\triangledown^{2}\psi+V\psi=i\hslash\frac{\partial }{\partial t}\psi## Obviously, there is a laplacian in the kinetic energy operator. So, I was wondering if the equation was rearranged as...

This is a basic question, so probably easy to answer. The following from Wikipedia seems pretty standard while describing the Schrödinger equation: "...and Ĥ is the Hamiltonian operator (which characterises the total energy of the system under consideration)." On the other hand, from page 100 of...

I am trying to see how I can use the schrodinger equation to quantify the changes in the intensity of light. My closest guess is using the time dependent pertubation theory

Hi at all, I'm tring to solve Schrodinger equation in spherically symmetry with these bondary conditions: ##\lim_{r \rightarrow 0} u(r)\ltimes r^{l+1}## ##\lim_{r \rightarrow 0} u'(r)\ltimes (l+1)r^{l}## For eigenvalues, the text I'm following says that I have to consider that the...

I am interested in Schrodinger equation with the temporal element and the calculation of the probability when its depend on 3 variable coordinate and time? How to calculate it and norm it? Probability = (integral x,y,z...0 to infinity) * (integral t...0 to infinity)=1 ?

Hi everybody! I need to compute a C++ program for solve Schrodinger equation and calculate nuclear density. My nucleus is made up of only neutrons immersed in a potential of a harmonic oscillator. Schrodinger equation is: $$[-\frac{\hbar^2}{2m}\triangledown^2+V_{HO}(r)]\psi=E\psi$$ with...

If one considers the quantized levels of E, for the solutions to the Schrödinger eqn,, then I am wondering: what are the lowest possible energies that can occur for the Schrödinger eqn? I take the highest possible energy is at the classical limit, but is the zero-point energy the absolute...

I have reviewed the various posts on gauge symmetry in particular this one which is now closed. In this post there is the following link:http://www.vttoth.com/CMS/physics-notes/124-the-principle-of-gauge-invariance. This is a good read. However, there is some clarification I need. The...

Hi guys! For nuclear case, I need to write an Schrodinger equation in cylindrical coordinates with an total potential formed by Woods-Saxon potential, spin-orbit potential and the Coulomb potential. Schrodinger equation can be written in this form: $$[-\frac{\hbar^2}{2m}(\frac{\partial...

Hi, I noticed that the raising and lowering operators:\begin{equation} A =\frac{1}{\sqrt{2}}\big(y+\frac{d}{dy}\big) \end{equation}\begin{equation} A^{\dagger}=\frac{1}{\sqrt{2}}\big(y-\frac{d}{dy}\big) \end{equation}can be used to solve the eqn HY = EY However I am curious about something...

Dear all, sorry I made a new post similar to the previous post "Initial conditions..", however, a critical point was missed in the previous discussion: The initial conditions y(0)=1 and y'(0)=0 are fine and help in solving the Schrödinger equation, however, studying free electrons, the equation...

Hi, I am wondering if there exists some general initial conditions for solving the Schödinger eqn. for 1D free electrons ? Thanks!

Hi everyone! Please, I'm trying to understand the Schrodinger equation, and I've understood it this far, which which is a miracle, hehehe: (Laplacian)(psi) plus ((2phi)/h)^2.2m (E-V)(psi) I know that hbar = h/(2phi) But how that turns into (Laplacian)(psi)+2m/(hbar)^2.(E-V)(psi) My math...

Long ago I read on these forums that one cannot derive the Schrödinger equations because they're fundamental scientific laws. But I have noticed that I can generate them by making the following physical assumptions and then doing a trivial amount of substitution and differentiation: (1) \frac...

In fact I am not sure if this is the right place to ask such a question but I'm going to ask anyways, just tell me if I am in the wrong place. So I doing a little experiment with the Schröndinger's equation, but the problem is I can't find a certain function. You all know the Schrödingers...

Homework Statement I'm asked to show that the two dimensional plane wave (for constant C) \psi \left ( \mathbf{r} \right )=Ce^{-i\mathbf{k}\cdot \mathbf{r}} satisfies the Schrödinger equation: -\frac{\hbar^{2}}{2m_e}\frac{\mathrm{d}^2 \psi\left ( \mathbf{r} \right )}{\mathrm{d}...

My question is that how does the Schrodinger equation arise from the Heisenberg equation of motion in the quantum field formalism. These are from Hatfield's book. So I'm having some difficulties to reproduce (2.36) by plugging (2.55) into (2.37) primarily because H is an integral...

Homework Statement I am currently reading a textbook on solving the Schrödinger equation for the harmonic oscillator using the series method; $$-\frac{\hbar^{2}}{2m}\frac{\mathrm{d}^2 \psi }{\mathrm{d} x^2}+\frac{1}{2}m\omega ^{2}x^2\psi =E\psi $$ It starts by using these two dimensionless...

So, I am a newbie in quantum mechanics, took modern physics last fall for my physics minor. I know that Schrodinger based his equation based on the equation K + V = E, by using non-relativistic kinematic energy (P2/2m + V = E) p becoming the operator p= -iħ∇ for the wave equation eigenfunction...

Homework Statement An electron coming from the left encounters/is trapped the following potential: -a<x<0; V=0 0<x<a; V=V0 infinity elsewhere the electron has energy V0 a)Write out the wave function b)normalize th wave function Homework EquationsThe Attempt at a Solution for -a<x<0...

Hi All, Perhaps I am missing something. Schrodinger equation is HPsi=EPsi, where H is hamiltonian = sum of kinetic energy operator and potential energy operator. Kinetic energy operator does not commute with potential energy operator, then how come they share the same wave function Psi? The...

Homework Statement I was trying to solve the time-independent Schrodinger's equation for this well: http://i.imgur.com/C9QrvkX.png First I tried to look at cases where the energy of a particle is ##E < V_1##. Homework Equations Schrodinger's equation...

Ok for starters, I am sorry for the length of the question and jamming multiple questions in here i feel like my doubts are all related and it would be best just to put it all in one place instead of creating 2-4 topics. I'm beginning to feel confused with the amount of ways i see people...

For a given stationary cubic-quintic nonlinear Schrodinger equation, EU=-U_XX+G1|U|^2U+G2 |U|^4 U, where X=X(t,x). There are bright and dark solitons. In many references, it is found that there is typo or mistake in dark soliton by substituting their soliton solution to this above eqaution. The...

The Nonlinear Schrodinger Equation (NSE) is presented as: $$i\frac{∂A}{∂z} = \frac{1}{2}β_2\frac{∂^2A}{∂t^2}-\gamma|A^2|A$$ The steady state solution $$A(z)$$ Can be derived as an Ansatz given by: $$ A(z) = \rho(z)e^{i\phi(z)}$$ By substituting and solving the ODE, the steady state...

okay so i need some help interpreting some of the results, so (-ħ2/2m)Ψ''=E-V0Ψ; So i set k2= 2m*(E-V0)/ħ2 and so : Ψ''=-k2Ψ so if V0=0 or is smaller than E, k2 is positive; *need for help starts here* Ψ=Aeikx+Be-ikx; another result for this would also be only eikx so is the second term only...

Homework Statement Homework EquationsThe Attempt at a Solution It is a short question so I don't suppose it is difficult. However, I don't really understand what it is asking for : 1.The TDSE itself is already a 2nd-order differential equation (if you substitute the terms back into H). 2...

Homework Statement [/B] Q18. Which of the following statements about Schrodinger equation is true? A) The exact solution of the equation never exists B) It is only applicable to the hydrogen-like atoms C) We can know the energy of the atomic orbital by solving the equation D) The square of the...

Homework Statement I'm a pharmacologist and I have a modern physics course to do. This is not my field and I'm completely lost... We were given this problem to do. Thanks a lot in advance. Consider a potential where U(x) = 0 for x ≤ 0 U(x) = -3E for x > 0 Consider a particle of energy E...