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Questions tagged [quantum-mechanics]

For questions on quantum mechanics, a branch of physics dealing with physical phenomena at microscopic scales.

Quantum mechanics, also known as quantum physics or quantum theory, deals with classical physical phenomena at quantum scales.

The precise nature of the subject has changed over the years. This article explains its current formulation.

Quantum mechanics aims toprovide a mathematical description of the dual particle-like and wave-like behaviors and interactions of energy and matter.

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Assumptions of Reynolds transport theorem

I have a question about Reynolds transport theorem https://en.wikipedia.org/wiki/Reynolds_transport_theorem $$\frac{d}{dt}\int_{\Omega(t)}fdV = \int_{\Omega(t)} \frac{\partial f}{\partial t} dV + \int_{\partial\Omega(t)}(v^b . n)fdA $$ where $f =…
user842424
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2 dimensional quantum harmonic oscillator and the associated energy levels

What I know so far: If $V(x,y)=\frac{1}{2}m(\omega_1^2x^2+\omega_2^2y^2)$ where $V$ is the potential in Schrodinger's Equation as usual, then $E=E_n=(n_1+\frac{1}{2})\hbar\omega_1+(n_2+\frac{1}{2})\hbar\omega_2$. Furthermore, if $w_1=w_2=\omega$…
UnsinkableSam
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What is the most general and abstract statement of "quantization" in quantum mechanics?

When I read physics explanations of "quantization", I am confused, because they talk about particles, momentum, and other specific things. It seems to me that quantum formalism is much more general than this (e.g. in quantum computing there are no…
user56834
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Schrödinger equation in momentum representation

I have the time independent Hamiltonian $$\hat{H}= c_{1} \hat{q} + c_{2} \hat{p}, \tag{1} \label{1}$$ where $\hat{q}$ and $\hat{p}$ are the position and momentum opertors. Thus, the one dimensional Schrödinger equation for a function $f(q,t)$ in…
Julio Abraham Mendoza Fierro
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normalising a wave function from Schrodinger's equation

Say $\psi(\vec r,t)$ is a separable solution that satisfies the Schrodinger's equation such that $\psi(\vec r, t)=\phi(\vec r)f(t)$. Then my book said "$\psi$ is normalised if $\int_{\mathbb{R^3}}|\psi|^2d^3x=1$", which is slightly conflicting since…
UnsinkableSam
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Dirac's notation? (QM)

I have a question regarding Dirac's notation in quantum physics. As far as I understand: $\langle a|b\rangle=(a1^*,a2^*)*(b1,b2)^T$ But what does $\langle1/2,1/2|J|1/2,-1/2\rangle$ mean?
Federico Scanagatta
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Confusion regarding $|A|^2 \int\limits_{-\infty}^\infty e^{i(p-p')x/h}=|A|^2 2\pi h\delta(p-p')$

The book "Introduction to Quantum Mechanics (Second edition)" by Griffiths says the following on pg 103: $$|A|^2 \int\limits_{-\infty}^\infty e^{i(p-p')x/h}=|A|^2 2\pi h\delta(p-p')$$ Here $\delta$ is the delta function. How is this true? If…
Ryan Hendricks
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Insert a Unitary operation between two others

Let's say I have two unitary operations $U_1$ and $U_2$, which together give a rotation of the following form: $$ U_1\cdot U_2 = \begin{pmatrix} e^{i\varphi} & 0 \\ 0&e^{-i\varphi} \end{pmatrix} $$ Now I want to insert a 3rd unitary matrix of…
Mechanix
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Heisenberg Picture for 1D Simple Harmonic Oscillator

The Halmiltonian for 1D simple harmonic oscillator is $$ H = \frac{1}{2m}(P^2 + m^2 \omega^2 X^2). $$ Show that in the Heisenberg picture, the sum of expectation $$ \langle X_{t+\pi/2\omega}^2 \rangle + \langle X_t^2 \rangle $$ is constant. Sorry…
Bernoulli
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Finding the Eigenvectors from a matrix with known Eigenvalues

I have a matrix called Ω. This is the matix: $$\frac 1 2\begin{bmatrix}2 & 0 &0\\0 & 3 &-1 \\0 & -1 & 3\end{bmatrix}$$ It's eigenvalues are known (I have calculated them earlier). They are $l_1 = l_2 = 1$ and $l_3 = 2$ I want to find the…
user1584421
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Which Area of Math Contributes to Quantum Theory

Hello Math Community, Thank you for taking the time to read my question. It is much appreciated. I'm curious as to which branch of mathematics would help develop our understanding of quantum theory ( quantum mechanics, spatial orientation of…
shiff desta
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Schrödinger equation energy level

Currently going through an old question which concerns a particle of mass $m$ on the interval $[-a,a]$ with potential $V=V_0$. In the question it says to show that the energy levels of the particle are $E=V_0+\frac{n^2\pi^2\hbar^2}{8ma^2}$, but…
Derren
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How to model this system of $^{238}\,U$ atoms?

An exercise from The Physics of Quantum Mechanics by James Binney and David Skinner I am now tying to solve this question. I cn find out the probability of trasmission and rebouncing for that $\alpha$ particle. However, how can I use the condition…
Ma Joad
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How many photons hit 1 square metre aerial

A question on an introductory text to quantum mechanics asks me to calculate the number of photons striking a $1$ metre square aerial each second at a distance of $1000km$ from a $200kW$ transmitter that broadcasts radio waves at a frequency of…
Deke
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Confirming wave function for particle on a sphere

The Hamiltonian operator for a particle with mass m on a sphere with radius $r_0$ can be written as: $\hat{H}=-\frac{\hbar^2}{2mr_0^2}\hat{\Lambda}^2$ where $\hat{\Lambda}^2=\frac{1}{sin^2\theta}\frac{\partial ^2}{\partial…
ChemGuy
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