# Tagged Questions

For questions on quantum mechanics, a branch of physics dealing with physical phenomena at microscopic scales, where the action is on the order of the Planck constant.

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### Intuition behind definition of spinor

Some time ago I searched for the definition of spinors and found the wikipedia page on the subject. Although highly detailed the page tries to talk about many different constructions and IMHO doesn't ...
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### Complex conjugate part of TISE

i would like to ask about complex conjugate part of this equation why ? I know that and so
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### Introductory book on probability for physicists

I'm a physics student looking to start learning more about probability. Is there some introductory book on measure theoretical probability theory that includes sections on quantum probability? To ...
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### Two operators $X$ and $Z$ in an infinite dimensional Hilbert space satisfying $X^2=Z^2=I$ and $\{X,Z\}= 0$

I am seeking to extend the following theorem to the case of infinite dimensional Hilbert space: Suppose we have two Hermitian operators $X$ and $Z$ in a finite dimensional Hilbert space $\mathcal H$. ...
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### Dirac Notation Confusion [closed]

I am trying to express the vectors $0\choose 1$ and $1\choose 0$ in dirac notation wrt the basis {|$0\rangle,$|$1\rangle$} How do I distinguish between the above two vectors given that all vectors ...
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### Example of a Projection Operator in $\mathbb{R^3}$

I'm looking for an operator $\hat P$ in $\mathbb{R^3}$ such that $\hat P^2=\hat P$ that is also Hermitian
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### Book Recommendation for Poisson Manifold and Deformation Quantisation

Can someone please recommend a basic introduction to the concept of Poisson Manifolds and Deformation Quantization. I'm new to Theoretical Physics and had to go through a lot of books before I even ...
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### Riesz representation theorem finite dimnesional case

I am taking a Quantum Mechanics course not a Functional Analysis course so I have only had a very basic introduction to Hilbert Spaces. I don't understand where the if and only if statement arises ...
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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 ...
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### Showing a orthogonal basis is complete

$\psi_1 = \frac{1}{\sqrt{2}}$ $\psi_2 = \sqrt{\frac{3}{2}}x$ By shwoing that any arbitrary function $f(x)=ax+b$ can be represented as linear combination of $\psi_1$ and $\psi_2$, show that $\psi_1$...
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### general two-state system

Consider a two-state system: The Hamiltonian takes the general form $$H= \begin{pmatrix} a_1 & c-id \\ c+id & a_2 \\ \end{pmatrix}$$ where $a_1, a_2, c, d \in\mathcal{R}$ $H$ can be ...
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### Momentum is quantised in compact spaces?

Background One of the first examples given when studying quantum mechanics is the particle on a cylinder, or particle on a ring. One finds that because of the periodic boundary conditions, ...
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### How does Ornstein-Uhlenbeck arise in quantum mechanics?

The Ornstein-Uhlenbeck operator, defined here is a self-adjoint operator on $L^2(\mathbb R^d)$ (with respect to Gaussian measure). I've heard it comes up in QM, and I'm wondering how? Does it ...
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### Differential equation

Hello if I have differential equation which is a function of x = differential equation which is function of t Can I say that the differential equation which is function of x = C= the ...
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### How to prove the Weyl identity?

In the post, there is a formula called Weyl identity: \begin{align} e^{-\frac{k}{n}a_n z^{-n}} e^{\frac{\ell}{n} a_{-n} w^n} = e^{\frac{\ell}{n} a_{-n} w^n} e^{-\frac{k}{n}a_n z^{-n}} e^{\frac{k\ell}{...
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### How to normalize the order of an expression?

Suppose that for $p, p'>0$, $i,j>0$, \begin{align} [y_{i,p}, y_{-j, p'}] = -\frac{1}{p}(1-q_1^{p})(1-q_2^p)\tilde{c}_{i,j}^{[-p]} \delta_{p,p'}, \end{align} where $\tilde{c}_{ij}^{[-p]}$ is some ...
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### Why is $\sum{\frac{1}{(j/2)!}(\xi)^j}\approx\sum{\frac{1}{j!}(\xi)^{2j}}$?

Why is $\sum{\frac{1}{(j/2)!}(\xi)^j}\approx\sum{\frac{1}{j!}(\xi)^{2j}}$? This equation is used for solving the Schrödinger equation of the harmonic oscillator at one point in Griffiths, ...
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### Prove: the density operator of a pure state has exactly one non-zero eigenvalue equal to unity

What is the proper way of proving : the density operator $\hat{\rho}$ of a pure state has exactly one non-zero eigenvalue and it is unity, i.e, the density matrix takes the form (after diagonalizing):...
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### Solving $\ddot{x} + \omega^2x = 0$: Classical Path for a Simple Harmonic Oscillator

I have posted in Math rather than Physics as the problem is mainly abuse(?) of trig identities rather than physics. This comes from an exercise within some lecture notes on Feynman Path integrals and ...
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### Functional integration and Feynman path integrals in wolfram alpha

Is it possible to do Feynman path integrals in wolfram alpha? Say for a free quantum mechanical particle. The reason I am interested in this is because I would like to see how it arrives at the ...
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### Lorentz transformation proof

For an occurence, we can choose coordinates ct and x (calculating both time and space in length) ct and x thereby take on the form of a two dimensional vector. Show that the same coordinates in S' ...
The Kronecker Delta is commonly used to represent a diagonal matrix: $$a_i \delta_{ij}=\left( \begin{array}{ccc} a_1 & 0 & 0\\ 0 & a_2 & 0\\ 0 & 0 & a_3 \end{array}\right)$$ ...