All Questions
Tagged with wavefunction schroedinger-equation
1,243
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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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votes
2
answers
64
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Quantum Mechanical Current Normalisation
Consider an electron leaving a metal. The quantum-mechanical current operator, is given (Landau and Lifshitz, 1974) by
$$
j_x\left[\psi_{\mathrm{f}}\right]=\frac{\hbar i}{2 m}\left(\psi_{\mathrm{f}} \...
- 713
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Hydrogen radial equation solution's boundary condition for $r \to 0$ [duplicate]
I am studying the hydrogen atom and I am analysing the radial equation: $$\left[\frac{-\hbar^2}{2m} \frac{\partial^2}{\partial r^2} + \frac{\hbar^2l(l+1)}{2m}+ V(r)\right]u=Eu$$ with $V(r)$ equal to ...
- 41
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3
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Negative kinetic energy on a step potential
I'm doing an introductory course on quantum mechanics. I'm having trouble with the explanation of the kinetic energy on the classically forbbiden region on a step potential ($V=0$ for $x<0$, $V=V_0$...
- 73
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2
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Time derivative of complex conjugate wave function [duplicate]
We have
$$\frac{\partial \Psi}{\partial t} = \frac{i\hbar}{2m} \frac{\partial^2 \Psi}{\partial x^2} - \frac{i}{\hbar}V\Psi$$$$\frac{\partial \Psi^*}{\partial t} = -\frac{i\hbar}{2m} \frac{\partial^2 \...
- 297
2
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1
answer
106
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Derivation of Schrödinger equation in Feynman-Hibbs
I am going through the derivation in chapter 4-1 of "Quantum Mechanics and Path Integrals. Emended Edition" by Feynman and Hibbs. The chapter starts with a proof of the equivalence of the ...
- 131
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$\pi$ phase shift upon reflection in quantum wells
Is there a similar phenomenon to the $\pi$ phase shift experienced by light upon reflection from a medium of lower to higher refracted index for particles in different potentials?
For instance, does a ...
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32
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Eigenstates of the Laplacian and boundary conditions
Consider the following setting. I have a box $\Omega = [0,L]^{d} \subset \mathbb{R}^{d}$, for some $L> 0$. In physics, this is usually the case in statistical mechanics or some problems in quantum ...
- 1,131
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How does 1D Schrödinger equation arise out of the postulated 3D Schrödinger equation and solving 1D particle using 3D Schrödinger equation?
I've stumbled upon this question when I was trying to solve the Schrödinger equation for a particle confined to a 1D line with some given time independent potential $V(x)$.
The energy eigenstates ...
- 109
2
votes
1
answer
65
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Plane waves, angular momentum, and the 2D Schrödinger equation
I've been thinking about the 2D Schrödinger equation for a free particle, particularly in polar coordinates, and the particular solution
$$\Psi(r, \phi) = J_1(r)e^{i\phi}.$$
This solution has an ...
- 789
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2
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Normal Base for Hilbert Space of delta Potential Well
I'm interested in the problem of an attractive $\delta$ potential. The Hamiltonian is given by
$$
H = - \frac{\partial_x^2}{2m} - V \delta(x).
$$
Solving this typically entails looking at scattering ...
- 25
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1
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46
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Regarding to the asymptotic solution of quantum harmonic oscillator
In quantum mechanics, the radial equation of the SHO takes the form
\begin{align}
\frac{d^2 u}{dx^2}+\left(\epsilon-x^2-\frac{l(l+1)}{x^2}\right)u=0,
\end{align}
where $x=\sqrt{\frac{m\omega}{\hbar}}r$...
- 27
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2
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Is the spherical outgoing wave solution to the Schrodinger equation not a member of $L^2$?
I was reading a discussion about the Mott problem, where the authors discuss the outgoing spherical wave solutions to the Helmholtz equations $\nabla^2 f = - k^2 f$. This equation can also be ...
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2
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Why is the time derivative of the wavefunction proportional to a linear operator on it? [closed]
I am currently trying to self-study quantum mechanics. From what I have read, it is said that knowing the wave function at some instant determines its behavior at all feature instants, I came across ...
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Proof that separation of variables leads to a complete basis of wave function in spherical coordinates [duplicate]
In griffith's introduction to quantum mechanics (chapter 4), there is an analysis of the stationary states of a particle given a potential function $V(r)$ that only depends on the radial distance $r$, ...
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