# Questions tagged [schroedinger-equation]

Partial differential equation which describes the time evolution of the wavefunction of a quantum system. It is one of the first and most fundamental equations of quantum mechanics.

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### Is gravity caused by the length contraction of a wave in an inelastic but tensioned medium? [closed]

As far as I know, all waves require medium through which they are propagated. A medium that couples two adjecent points in space together, so that the change in amplitude of one point causes a change ...
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### Does rotational symmetry imply reflection symmetry for electrostatic interactions?

Consider two charge distributions $\rho_A(\mathbf{x})$ and $\rho_B(\mathbf{x})$. Suppose that the ground state energy of a system of $n$ electrons in a potential generated by the sum of these two ...
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### Can a wave function discontinuous in the time variable be a solution of the Schrödinger equation?

It is well known that wave functions that are discontinuous in the space variable cannot be solutions of the Schrödinger equation, because the Schrödinger equation is a second-order differential ...
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### Quantum mechanics with a classical Chern-Simons term

In this post, quantum mechanics falls under what is traditionally called "first quantization". This is in contrast to quantum field theory which traditionally falls under "second ...
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### Why can non-differentiable solutions to the Schrödinger equation be ignored?

To clarify the question, let's consider the particle in a box (infinite potential $V$ outside [0,1], potential 0 inside [0,1]). (But the problems illustrated here also apply to particles in a non-...
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### How to Derive the Time Evolution Equation for Quantum Phase?

In quantum mechanics, the wavefunction $\psi(x,t)$ outputs a complex number that describes the probability amplitude of finding a particle in a particular place and time. The complex number can be ...
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### Time dependency of Wave function and its probability density function (PDF) [closed]

When we study the Schrodinger wave equation, we have a time dependent wave function $\Psi(x,t)$, and when we deduce its Probability Density function we come to know there is no time dependence in the ...
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### Uniform dynamics in quantum mechanics

I've found in the book "Quantum Processes System & Information" of Benjamin Schumacher the following definition of "uniform dynamic": it often happens that the basic dynamical ...
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### Correct way to take complex conjugate of the Schrodinger equation

There are one or two questions on this site regarding the complex conjugate of Schrodinger equation but they do not clear my doubt. Question : The Schrodinger equation is $$iħ \frac{∂Ψ}{∂t} = HΨ$$ ...
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### What, exactly, does Schrödinger's wave equation describe (just in plain English, without any of the math please) [closed]

I've been studying the philosophical foundations of quantum mechanics and would love to find out if my understanding is correct. Could anyone please let me know if the below description is accurate? ...
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### Equation of motion of quantum fluctuations/ quasi particles

I have a question in my mind, that is haunting me for some time now. I am looking for an equation of motion for a quasiparticle. My actual problem is originated in the Gross-Pitaevski model and the ...
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### Field theories where the potential solves a linear Schrodinger equation

Are there physical situations/applications where the potential solves a linear time-dependent Schrodinger equation, or where the gradient of a solution to the Schrodinger equation (after somehow ...
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### Calculating the expectation value of the angular momentum operator

I'm not looking for the exact answer to the question, but rather why a certain way of solving it is chosen. We agree on the answer, but why is the approach different. I'm afraid it's a sign of me not ...
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### Derivation of Schrödinger equation in Feynman-Hibbs

I am going through the derivation in chapter 4-1 of "Quantum Mechanics and Path Integrals. Emended Edition" by Feynman and Hibbs. The chapter starts with a proof of the equivalence of the ...
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### Unperturbed eigenvector combination for degenerate case in perturbation theory

My question has arised from the previously asked question. In short: I have Hamiltonian with a perturbation such that $\hat{H} = \hat{H_0} + \lambda \hat{V}$. I know eigenvectors for the unperturbed ...
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### How can I convert a non-local potential $V (r, r')$ into a local but energy-dependent potential, i.e., $V (r, E)$?

I need to localize a nuclear non-local potential. Using both these non-local and local potential in the Schrödinger equation we should have approximately close eigenvalues. I tried the way followed by ...
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### Is Schrodinger's cat a problem of how we define identity?

I apologize if the question is somehow silly or useless. I was reading about the infamous Schrödinger's cat paradox and I thought that if we consider that a cat is composed of numerous atomic ...
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### Does this double well potential contradict the fact that there is no degeneracy for one-dimensional bound states?

This example is taken from Modern Quantum Mechanics by Sakurai. Consider a symmetric double well potential in one-dimension with a barrier of height $V_0$ and width $a$ at the middle. The eigenstates ...
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### Finite-time effects in Landau Zener

Consider a two level system with a Landau-Zener Hamiltonian of the form $$\hat{H}=\begin{pmatrix}v t&\beta\\\beta&-v t\end{pmatrix}.$$ The Landau-Zener formula provides a closed form for the ...
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