# Questions tagged [quantum-mechanics]

Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.

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### How do you account for all the photons and plethora of quantum particles in the box between the double slits and the back wall?

Does the particle being shot not interact with the all the particles that must be consuming the space in the box before the back wall? How do we know it’s the same photon traveling the distance to ...
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### Invariant nature of mass and particle annihilation [closed]

Since mass is a Lorentz invariant, it can never change to preserve the vectorial nature of the four-momentum and the other four vectors. Thus the only interpretation of the energy-mass equation that I ...
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### Why does the minimum energy of motion in a Coulomb field differ from the theoretical value?

I would like to find the minimum energy of Coulomb potential motion using matrix method. $H=-\frac{1}{2}\Delta-\frac{1}{r}$ I have chosen Slater Type Orbitals as a basis functions $R(r)=Nr^{n-1}e^{-r}$...
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### The probability density function $|Ψ|²$ [duplicate]

Max Born stated that $|Ψ|²$ is the probability density of a particle, given its wave function to be $Ψ$. But why is this? Where does this come from?
1 vote
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### Correlation function and Green's function

I have referred to several materials on Green's function but I found those notions pretty confusing. Now what I have tried to do is to calculate the inverse matrix of $G^+(E)=E-H+\mathrm{i}\eta$ where ...
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### Relationship between $S$ matrix elements and $T$ matrix elements

In hadron physics, we define the $S$ matrix as $S=I+iT$, where $T$ is transition matrix. But on the question: Finding relation between matrix $S$ and matrix $M$ for wave propagation, it gave an ...
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### References on the difference between Dirac's and Von Neumann's approach to Quantum Mechanics (rigged Hilbert Space vs Hilbert Space only)

I have not found any clear and comparative explanation between the Dirac and von Neumann versions of Quantum Mechanics (rigged Hilbert Space vs Hilbert Space only). I have found some short articles. ...
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### Is the Hamiltonian some sort of connection/gauge field?

I'm not sure if this is a well-defined question, but I was just looking through some old notes and noticed that the Hamiltonian in usual QM has a similar transformation as gauge fields in QFT: under ...
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### Double-slit experiment: How do we know the particle effect comes from the nature of light rather than its interaction with the detector?

In the double-slit experiment, we shine a light wave through two closely-spaced parallel slits at a screen, and observe an interference pattern on the screen. We then reduce the intensity of the light ...
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### Formation of a hydrogen atom from delocalized electron and proton

From the initial state of an electron and a proton in a box. I would like to find a reasonable hamiltonian, or way to describe the interaction that leads to the formation of a Hydrogen atom. Here is ...
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### Can we study the angular momentum of a plane wave scalar particle?

In a plane wave we are in a $p_z$ eigenstate. I saw that $[L_z,p_z]=0$, but $[L^2,p_z] \ne 0$. Is it enough to say that the particle has a defined angular momentum along $z$?
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### Calculation of phase error

In papers on quantum sensing, I often see the following formula: $\delta \phi=\frac{\Delta M}{|\partial \langle M \rangle /\partial \phi|}$ (for example in this paper: Quantum-Enhanced Measurements:...
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### Reverse bias p-n junction diode and Kinetic energy

In reverse bias p-n junction diode, which energy is lower than the energy of the potential barrier: the average kinetic energy of the would-be-tunnelling electrons or the kinetic energy of the ...
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### Rotations and angular momentum

Cohen tannoudji. Vol 1.pg 702 "Now, let us consider an infinitesimal rotation $\mathscr{R}_{\mathbf{e}_z}(\mathrm{~d} \alpha)$ about the $O z$ axis. Since the group law is conserved for ...
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