# 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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### First order state correction for time independent perturbation theory

Following the derivation on the wikipedia page, https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics)_ , $|n_{0}\rangle$ is an eigenstate of the unperturbed Hamiltonian $\hat{H}_{0}$, ...
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### Question about quantum mechanics and diatomic molecule

"The double well is a very primitive one-dimensional model for the potential experienced by an electron in a diatomic molecule (the two wells represent the attractive force of the nuclei)" ...
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### Combine the completeness and linearity of Schrodinger equation's solution, can we say that any wavefunction can solve any Schrodinger equation?

From quantum mechanics, I learnt: Completeness of energy eigenfunction: The energy eigenfunctions of the Schrodinger equation span the space, i.e. any state can be expanded as linear combination of ...
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### How can Schrodinger equation be derived based on the argument of Lorentz transformation?

I came across this note which talk about obtaining the Schrodinger equation based on the argument of Lorentz transformation. However, I am not able to follow how it exactly works. Any help would be ...
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### If arbitrary wavefunctions can be expanded as energy eigenfunctions of a schodinger equation, is it mean that it can solve schodinger equation anyway? [closed]

We know that the superpostion of solutions also sloves the schodinger eq, and any wavefunction can be expended as superposition of energy eigenstates. Is it means that any wavefunction can solve the ...
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### Solving Schrodinger Equation for scattering off a periodic potential

I am interesting in solving the time-independent Schrodinger equation (TISE) for the scenario where we have an electron plane wave of fixed energy incident upon a potential that is infinite and ...
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### Isn't it inaccurate to use the Schrödinger equation to find the probability that a macroscopic object will undergo quantum tunneling?

Since Schrödinger's equation doesn't show wavefunction decay or quantum decoherence, isn't it inaccurate to calculate the probability that a person or macroscopic object will quantum tunneling? I ...
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Playing around with the Schrödinger equation, I separated the time partial derivative this way: $$\frac{\partial \Psi}{\partial t}=\frac{i\hbar}{2m}\frac{\partial^2\Psi}{\partial x^2}-\frac{i}{\hbar}V\... • 592 10 votes 4 answers 2k views ### Are there any nonlinear Schrödinger equations? The 1D Schrödinger equation reads:$$\frac{\partial \Psi}{\partial t}=\frac{i\hbar}{2m}\frac{\partial^2 \Psi}{\partial x^2}-\frac{i}{\hbar}V\Psi. Now, generally we have $V=V(x)$ (or it dependending ...
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I have read in Griffiths' Quantum Mechanics that there is a phenomenon called tunneling, where a particle has some nonzero probability of passing through a potential even if $E < V(x)_{max}$. What ...