I'm trying to solve the Schrodinger equation in cylindrical coordinates using this potential $V=\frac{c}{\rho}$ where c is a constant. $$\psi(\rho,\phi,z)=R(\rho)\Phi(\phi)Z(z)$$ The $\phi$ and Z part are simple to solve but in the radial part I get this: $$ \rho\frac{1}{R}\frac{\partial}{\par...

I'm trying to satisfy the following equality involving pauli matrices: $V = A\frac{\vec{\sigma_1}\cdot\vec{\sigma_2}r^2-3(\vec{\sigma_1}\cdot\vec{r})(\vec{\sigma_2}\cdot\vec{r})}{r^5} = 2A\frac{S^2r^2-3(\vec{S}\cdot\vec{r})^2}{r^5}$, given that $\vec{S} = \frac{1}{2}(\vec{\sigma_1}+\vec{\sigma_...

According to this paper, there's no consistent treatment of the two-slit experiment: It is true that the usual textbook discussions of the two-slit experiment are riddled with ambiguities and omissions; and this is for the reason that a consistent, quantum-mechanical treatment of the two-slit...

Suppose there are two inertial reference frame, a and b. a and b initially approach each other at a constant velocity, +v. Two observers, one in a, the other in b, starts their stopwatch at exactly the same moment when they are at the same position. From that point, a and b starts moving away f...

I found how to rewrite the state of the qubit and qutrit. I found qudit's, (link below) reassuring me the promsing field of QKD (of which is particular interest with research in QKD). I now found new data that lead me to the ququat. How is the ququat written? Is it similar to the qubit and qutr...

When a photon encounters a mirror, I understand that it picks up a phase shift. So, for example, a linearly polarized photon will become circularly polarized. When we're considering the "which-path" information of a photon in a Mach-Zehnder interferometer, we usually see it described as undergoi...

There are currently 17 known particles in the Standard Model. How were all these particles theorized ? Which experiments did physicists used to prove the existence of these particles? What kind of setups does physicists use to identify new particles?

I am trying to understand how I can obtain the correct band structure of fermions hopping on a lattice when choosing larger cells for a crystal. As a toy model, we can consider a chain … o---o---o---o … with Hamiltonian $H=\sum_{\langle i j \rangle} c_i^\dagger c_j + h.c. = \sum_i c_i^\dagger c_...

Why does a unit modulus complex number multiplied by wave function represent the same state? Thanks for the help.

I was recently introduced to the concept of probability as a conserved quantity in the context of QM, and the mathematics behind using the continuity equation on probability (specifically, $\nabla \bullet \mathbf{J} + \frac{\partial |\psi|^2} {\partial t} = 0$). Eventually, we came to the well-...

I have given the following Hamiltonian with periodic potential. $H={P^2}/{2m}+V$ where $V$, I have drawn below, I want make a variational approximation of the ground state energy.Also, I have given that the magnitude of the trail wave function should have following properties in $0<x<2a$ $|...

I have a textbook giving an example of what the probability is of observing system Ψ = a|A⟩ + b|B⟩ in states a|A⟩ and b|B⟩. I'm not sure I understand it fully. How do I use the Born rule to know the probability of observing system Ψ = a|A⟩ + b|B⟩ + c|C⟩ in the state c|C⟩ ? Could someone please gi...

Please give me your thoughts regarding the statement and questions that follow: A light wave is a probability wave depicting where a photon is likely to be within the wave. Once the photon is found then all other possibilities are gone. Given this, is it then true to say that one light wave will ...

I need websites or books that has quantum mechanical exercises in particular that finds the total angular momentum eigenvalues s,m (for example two spin 1/2 systems). Do you know where i can train?