Linked Questions

3
votes
0answers
82 views

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 ...
12
votes
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 ...
6
votes
2answers
5k views

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 ...
4
votes
3answers
1k views

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 ...
3
votes
4answers
3k views

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 ...
2
votes
2answers
1k views

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 $T$ ...
2
votes
1answer
1k views

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 ...
7
votes
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 ...
2
votes
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 ...
2
votes
0answers
1k views

Scattering on delta function potential

Suppose a particle has energy $E>V(+/-\infty)=0$, then the solutions to the Schrodinger equation outside of the potential will be $\psi(x)=Ae^{i k x}+Be^{-i k x}$. How can one show or explain that $...
0
votes
1answer
389 views

Probability flow at any point of a free particle stationary wave in one-dimension!

Update The plane wave state for a free particle given by $\psi(x,t)=A\exp[i(kx-\omega t)]$ is completely delocalized in space and time. Therefore, the wavefunction is present everywhere in space at ...
4
votes
2answers
91 views

Contradiction between aymptotically free particles in QFT and unlocalization

When studying different interactions in any QFT, one always assumes that the IN and OUT states are asymptotically free particles with definite momenta. For example, one assumes that an electron and a ...
1
vote
3answers
119 views

Finite square wall with $E > V_0$

I'm working through a problem for homework and feel as if there is a typo or I am confused. The problem is with a one sided finite square wall such as this: So the energy is more than $V_0$. I'm ...
1
vote
1answer
144 views

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 ...
3
votes
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 ...