# 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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### Vector operator formulation

I showed that the ladder operators: $\hat{\overrightarrow{a}}=(a_x, a_y , a_z)$ and $\hat{\overrightarrow{a}}^{\dagger} = (a_x^{\dagger}, a_y^{\dagger} , a_z^{\dagger})$ can form a vector operator by ...
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### Momentum in Classical mechanics and quantum mechanics

In the following question $\nabla, \hbar$ means gradient r(position vector) and reduced Plank's constant respectively.
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### Where did quantum numbers arise from?

I was told that there are 4 quantum numbers which help in locating the position of an electron inside an atom. And they are Principal quantum number Azimuthal quantum number Spin quantum number ...
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### How do we choose the basis of an Hilbert Space?

When we define a basis for the Hilbert Space for a spin half particle I understand it being done using the principle of mutual exclusivity that is if $S_z = +\hbar/2$ then it cannot be $S_z = -\hbar/2$...
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### What does the term "condense" mean in the physics literature

When reading the physics literature, we often see the term "condensate". Some examples: in the string net model (Wen, Levin), one will say the string "condensate". in QCD, people ...
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### Is This Quantum Eraser Video from Fermilab Incorrect?

In a video from Don Lincoln of Fermilab here, the following claim is made about a quantum eraser-type setup (about 2 min 50 sec in): "If A & B are turned off, you see a wave pattern. That ...
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### Heisenberg’s Formulation of Quantum Mechanics and Particle Trajectories [duplicate]

In the article, under the history section, Heisenberg recounts a discussion with Einstein regarding Heisenberg’s matrix mechanics: “ He pointed out to me that in my mathematical description the notion ...
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### Average squared of angular momentum

Consider spin $S$ particles. Is there an easy way to prove that $\langle \vec{S} \rangle \cdot \langle \vec{S} \rangle \leq S^2$ for all states? I understand intuitively that the bound is realized ...
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### On the invariance of $\rho |\psi \rangle$? (For Wigner and his friend)

Motivation So let's say I shoot circular polarized light which is either right $| R \rangle$ or left $| L \rangle$ polarized. My friend notices that I choose left and right equally $50$% of the time. ...
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### Measure Position of Electron Directly

What is the most directly way to measure the position of free electron in an expirement? I don't asking about theoretical suggestion but rather on practical expirement which people have done.
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### Questions on quantum spin [closed]

I﻿ have been researching quantum physics by myself through books and videos and I can understand the property of particle “spin” but only to a limit. I understand it’s intrinsic angular momentum and ...
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### Normalizer of $SU(2)\times SU(2)$ in $SU(4)$

What is the normalizer of $SU(2)\times SU(2)$ in $SU(4)$ or how would I find it? Reason for the question: with 2 qubits, if I was interested in conjugation of 2-qubit gates with generic $SU(2)$ ...
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### Can weak measurement principles of Quantum mechanics be used in similar questions in classical estimation problems?

This is a surface level question and I don't want to go into detail. Imagine an algorithm which when used with a sensor output gives the statistical moments of a variable in nature (for example mean ...
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### What would be the proper distribution to model the number of particles in a state in canonical ensemble

Suppose my system has $N$ particles, and I want to find a distribution for $n_i$, the number of particles in the $\epsilon_i$ energy state. What I do know is the boltzmann probability, which tells me ...
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### Arbitrary helicity in the nonrelativistic quantum free particle

One of the Casimir operators of the Euclidean group $E(3)$ is $\vec{J}\cdot\vec{P}$. For a quantum free particle (described in abstract as) $|p,\lambda,\hat{\vec{p}}\rangle$, the given Casimir ...
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### How Heisenberg defined the $P$ $Q$ matrices terms?

I learnt in some Wikipedia articles that the terms of the $P$ and $Q$ matrices designed by Heisenberg, were composed of Fourier coefficients. Could you provide some explanation on how these ...
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### Measuring a qubit in the wrong basis

I'm a computer scientist and right now I'm trying to end the research work for my master thesis and a basic problem of quantum mechanics is blocking me. I'm trying to do a probability calculus of the ...