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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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How was the $O(\epsilon ^2)$ term obtained?

$$\newcommand{\brak}[1]{\left\langle #1 \right\rangle}$$ I'm trying to study Path Integral approach to Quantum Mechanics on my own, during the readings, I came across one part that I'm not certain how it was exactly derived, could use any possible…
Gvxfjørt
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Operators and Commutators in Quantum Mechanics

I'm trying to understand the terms "Operators" and "Commutators". Operators / Variables helps us to derive a differential equation that our wave equation must satisfy. Ex. Momentum Operator $P = \frac{\hbar}{i} \frac{\partial}{\partial x}$, Energy…
rndflas
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Quantum theory linearly independent solutions

I'm trying to do the part of this qusetion where we need to find two linearly independent solutions to (2) of the given form. Is there a nicer way to do it other than just plugging it into (2). I was thinking of trying to pick B=0 for one solution,…
lkjhgfdsa
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Normalize wave function and check if it is in Hilbert space

Consider a particle of mass m freely propagating within the box x ∈ [0, R]. Prepare the particle in the state corresponding to the wave function $ \psi (x) Asin(\frac{3\pi x}{2R}) cos(\frac{\pi x}{2R}) $ inside the box, and vanishing outside.…
italy
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Re-writing in sign basis.

$\newcommand\ket[1]{\left\vert #1\right\rangle}$ Let $\ket\phi = 12 \ket{0} + 1 + 2\sqrt{i2}\ket{1}$. Write $\ket\phi$ in the form $\alpha_0\ket{+} + \alpha_1\ket{-}$. What is $\alpha_0$? I came across this problem in a course i am doing, i have…
fosho
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N-Representation of an Operator

Calculating $\langle{n} \; {| \; \hat{X}^2 \; |} \; m\rangle$ in the N-representation, where $| \; m\rangle$ and $| \; n\rangle$ are harmonic oscillator states and $\hat{X} = \sqrt{\frac{\hbar}{2mw}}( \hat{a} + \hat{a}^\dagger )$, I find that : $ \;…
Surtr
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$\frac{d^2}{dx^2} = \lim_{\delta x\to 0} [f(x-\delta x) - 2f(x) + f(x+\delta x))/\delta x^2]$ find a matrix

Given that $$\frac{d^2}{dx^2} = \lim_{\delta x\to 0} [f(x-\delta x) - 2f(x) + f(x+\delta x))]\cdot\frac1{\delta x^2}$$ find an appropriate matrix that could represent such a derivative operator, in a form analogous to the first derivative operator…
user315245
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Quantum mechanics question?

A particle of mass $m$ is confined within an infinite, one-dimensional potential well, $U(x)$, of width $a$. $$ U(x) = \begin{cases} \infty & x \leq \frac{-a}{2}, x \leq \frac{a}{2}\\[6pt] 0 & \frac{-a}{2} \leq x \leq \frac{a}{2} …
user145974
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quantum harmonic oscillator and the mean energy U(T)

The energy of a quantum harmonic oscillator is given by: $$E(n)=\hbar\omega\left(n+\frac{1}{2}\right)$$ The canonical partition function is given by: $$Z(T)=\sum_{n=o}^\infty e^{-\beta E(n)}=\sum_{n=o}^\infty e^{\frac{-\beta \hbar\omega}{2}}…
Hermes Chirino
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A simple quantum mechanical system

I am studying a Quantum Mechanics course and I have come across something that I am a little stuck on, mathematically. Physically it seems to make sense but I'm not sure which equations to use to justify the behaviour of the system. Here is the…
Ben Gerry
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Angular Momentum Operators: A quick question

Given $L_+|l,m\rangle \propto |l,m+1\rangle$ and $L_-|l,m\rangle \propto |l,m-1\rangle$ Why isn't it the case that $\langle l,m|L_+L_-|l,m\rangle = 1$? Perhaps naively, but I assumed $\langle l,m|L_+L_-|l,m\rangle = \langle l,m|L_+|l,m-1\rangle =…
Phibert
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How can I construct a $n\times n$ complex hermitian matrix?

As indicated in the title, I need to build a complex hermitian matrix of $ n \times n $ numerically, but I am somewhat lost and I don't know how to do it. Anyone have any ideas to build it?
Bathyalpelagic
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Find the energy eigenvalue from a given wave function

A particle of mass $m$ is trapped in an infinitely deep one-dimensional potential well between $x = 0$ and $x = a$, and at a time $t = 0$ it is described by the wave function $$ w(x,t=0) = \frac{1}{\sqrt{2}} \sin \left(\frac{\pi x}{a} \right)…
rosiegeorge
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