# Linked Questions

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### Why can quantum tunnelling be handled as a static problem? [duplicate]

Quantum tunnelling is a process that can happen in quantum mechanics but is forbidden in classical mechanics. Roughly speaking, a particle can possibly escape from a potential well or penetrate into a ...
5answers
18k views

### Confused over complex representation of the wave

My quantum mechanics textbook says that the following is a representation of a wave traveling in the +$x$ direction:$$\Psi(x,t)=Ae^{i\left(kx-\omega t\right)}\tag1$$ I'm having trouble visualizing ...
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### Why are scattering matrices unitary?

In Griffith's QM book, he introduces scattering matrices as an end-of-the-chapter Problem 2.52. For a Dirac-Delta potential $V(x) = \alpha \delta (x - x_0)$, I've derived the scattering matrix and ...
3answers
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### What is the direction of propagating waves of the form $e^{ikx}$?

Suppose we are given a wavefunction $$\psi(x) = Ae^{ikx} + Be^{-ikx}.$$ After some internet research I found that When coupled to the usual time-dependent energy (phase) factors in the full TDSE ...
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### Analytic solutions to time-dependent Schrödinger equation

Are there analytic solutions to the time-Dependent Schrödinger equation, or is the equation too non-linear to solve non-numerically? Specifically - are there solutions to time-Dependent Schrödinger ...
2answers
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### Probability current in scattering problems

This is a section from Wikipedia: In regions where a step potential or potential barrier occurs, the probability current is related to the transmission and reflection coefficients, respectively $T$ ...
1answer
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### Why is the reflection coefficient in quantum mechanical scattering defined this way?

In Griffiths' "Introduction to Quantum Mechanics, second edition" section 2.5.2, p. 73, he states: For the delta-function potential, when considering the scattered states (with $E > 0$), we have ...
2answers
750 views

### Why the cross section can be obtained directly from the stationary scattering states?

I'm currently studying scattering theory in the book Quantum Mechanics, Vol. 2 by Cohen-Tannoudji. In the book the author deduces that to find the number of particles detected far from the target at a ...
2answers
544 views

### Why does the wave description say that probability oscillates, while the phase interpretation says constant amplitude?

The wave description of a particle illustrates an oscillating probability of the particle being found in any point in space. When a particle travels, it carries along with it a phase that oscillates ...
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### Why we don't need to normalize the scattering states?

I am new to QM, have find some wavefunction in different potentials, but there we need to normalize the wave function, for a reason that - particle should be found somewhere . So a wave-function, to ...
1answer
107 views

### Solving the 1-d time-independent Schroedinger's equation with an infinite boundary

In my introductory modern physics class we have examined time-independent solutions to the Schrödinger equation in 1 dimension. We looked at a few cases without finite boundary, e.g., free particles ...