# Tagged Questions

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### Superposition principle

If $S=(v_{1},v_{2}......v_{n})$ is a basis for vector Space V, then every vector v in V can be expressed in the form of $v=c_{1}v_{1}+.......c_{n}v_{n}$ in an unique way. Explain the significance of ...
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### Modern physics photoelectric effect [closed]

In a photo electric experiment, energy of photon is 5eV incident on a metal surface. They liberate electrons which are just stopped by an electrode at a potential of -3.5V w.r.t the metal. The work ...
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### Uncertainty in the hydrogen ground state [closed]

The following question is put forward by one of my students. 1.In spherical polar coordinates, can radial momentum have the form $(h/2\pi i)[\partial/\partial r - 1/r]$? 2. If it is so, what is the ...
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### Finite Square Well Inside an Infinite Square Well

Ok here's a potential I invented and am trying to solve: $$V(x) = \begin{cases} -V_0&0<x<b \\ 0&b<x<a \\ \infty&x>a \\ \end{cases}$$ and $V(-x) = V(x)$ (Even ...
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### Idempotent Operators

If $P$ is an idempotent operator, $P^2 = P$ and we have a vector $|\psi\rangle$, $P\neq1$, and the relation $$PL |\psi\rangle = L|\psi\rangle,$$ what conclusions can we draw about $L$, which is a ...
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### I am trying to calculate how $<r>$ in the hydrogen atom evolves with time

I am working on the Hydrogen atom and I was trying to calculate $\frac{d<r>}{dt}$ using $$\frac{d<r>}{dt} = \frac{i}{\hbar} <[\hat{H} , \hat{r}]>.$$ Here $r = \sqrt(x^2 + y^2 + z^2)$ ...
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### Poles for a particle scattered in a delta potential

I am working on problem a professor gave me to get an idea for the research he does, and have hit a point where I'm having a difficult time seeing where I need to go from where I'm at. I would also ...
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### Angular momentum for 3D harmonic oscillator in two different bases

I know that the energy eigenstates of the 3D quantum harmonic oscillator can be characterized by three quantum numbers: $$| n_1,n_2,n_3\rangle$$ or, if solved in the spherical coordinate system: ...
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### CPT symmetries for a free Klein-Gordon equation and in minimal coupling

I'm studying for an exam on relativistic quantum mechanics and one of the issues to prepare is about symmetries of Klein-Gordon equation concerning $C$, $P$, $T$ transformations for a free field, and ...
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### Divergent solution in time-dependent Schrödinger equation

if I transform the time-dependent SchrÃ¶dinger equation without a potential I get: $$- \hbar \omega \psi(\omega,x) = \frac{- \hbar^2}{2m} \frac{\partial^2 \psi(\omega,x)}{\partial x^2}$$ The ...
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### Nuclear shell model - finite square well

I am trying to make a simplified approximation and solve Schrodinger equation in the finite square well to model the nucleus of Ca (shell nuclear model). The potential is $V(r) = -V_0$ for ...
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### Atom state vectors kets

An atom with two energy levels has 2 states (excited and ground), represented by kets $|e\rangle$ and $|g\rangle$ respectively. The atom has energy $\frac{1}{2}E_\theta$ when excited and ...
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### Determing what is differnece beetwen eigenvalues for attractive Coulomb Field (Hydrogen) calculated by exact method and WKB aproach

I have task to compare eignevalues gained by exact calculation on electron in Coulomb attractive field (hydrogen) and gained by WKB method.. As far as I get, eigenvalues gained with exact method are ...
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### 1D Infinite Square Well: Box Suddenly Increases in Size. How treat this?

I am currently working my way through John S. Townsend book "A Fundamental Approach to Modern Physics" (ISBN: 978-1-891389-62-7). Exercise 3.12 (p.111) is about the 1D infinite square well. The box ...
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### Center of mass coordinates in Lagrangians and Laplacians

Is there a quick nice and easy way to write Lagrangian's and the classical/quantum Laplacian operator in terms of center of mass coordinates? The algebra is so involved and it has me confused about ...
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### What is the eigenvalue of $J_z$?

In the calculation of the Zeeman Effect, the most important calculation is $$\langle J_z + S_z\rangle.$$ Suppose we want to find the Zeeman Effect for $(2p)^2$, meaning $l = 1$. In Sakurai's book, ...
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### Evaluation of expectation values

I will denote operators with hats. Suppose we got an operator of the form $i[\hat p, \tan^{-1}(e^{\hat x})]$ and we want to calculate the amplitude for a transition from a state $|p_i\rangle$ to the ...
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### How to quantize a rubber band stretched between two poles? [closed]

Consider a classical non-relativistic material string obeying Hooke's law stretched between two poles with either Neumann or Dirichlet or periodic boundary conditions and subject to either traversal ...
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### Galilean Transform

I tried to solve a problem using two different ways and I had some trouble, the problem is: We define a symmetry transform of the expected value of $\vec{P}$ like this: \langle \psi|\vec{P}|\psi ...
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### How does $p_x$ commute with $p_y$, i.e. $[p_x,p_y]=0$? [closed]

I know it's a simple and basic question but would someone show me how to evaluate $[\hat{p}_x,\hat{p}_y]$?