# Tagged Questions

In physics, an operator is almost always either a square matrix or a linear mapping from one space of functions (often on $\mathbb{R}^N$ or $\mathbb{C}^N$) to the same or other like space of functions. Operators serve as *observables* and as *time evolution operators* in Quantum Mechanics. This tag ...

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### What is $\langle \phi | H | \psi \rangle$ in QM?

I know that $\langle \phi | \psi \rangle$ is the probability of going from the $\psi$-state to the $\phi$-state, and that $\langle \phi | H | \phi \rangle$ is the expectation value of the energy for ...
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### Linear viscoelastic differential operators

I am starting with differential operators: $P = \sum_{i=0}^{N}p_i \cfrac{d^i}{dt^i}$ $Q = \sum_{i=0}^{N}q_i \cfrac{d^i}{dt^i}$ $p_i$ and $q_i$ are functions of time only. $K$ is a constant that ...
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### Complex conjugate of the Schrödinger equation?

This might be a very simple question but I don't understand how to compute the complex conjugate of the Schrödinger equation: $$i\partial_t \psi = H\psi$$ where $H$ is an hermitian operator. How to ...
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### Representing operators in the Glauber-Sudarshan P-representation

If $| \alpha >$ represents a coherent state (the normalized right eigenstate of the destruction operator $a$ in Quantum Mechanics; $\alpha$ is a complex number), then it is known that: \begin{...
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After reading Dirac's method for finding the eigen energies of a harmonic oscillator by means of ladder operators and commutation relations, I tried making some exercises on them. First I did a ...
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### Lower bound on energy is potential minimum

Suppose we have a particle of mass $m$ that is in an eigenstate $|\psi\rangle$ of the Hamiltonian $\hat{H}=\hat{T}+\hat{V}$, where $\hat{T}$ is the kinetic energy operator and $\hat{V}=V(\hat{r})$ is ...
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### Show that a linear operator can be written in terms of its spectral decomposition [closed]

Let $\hat Q$ be an operator with a complete set of orthonomal eigenvectors: $$\hat Q |e_n\rangle=q_n|e_n\rangle\ \ (n=1,2,3,...)$$ Show that $\hat Q$ can be written in terms of its spectral ...
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### Statement of vector model of angular momentum in Eisberg and Resnick

While serving as a teaching assistant for a sophomore-level Quantum Physics course, I came across the following paragraph in Eisberg and Resnick regarding orbital angular momentum (section 7-8, page ...
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### Clarification from Griffiths Introduction to quantum mechanics

A question from Appendix Linear algebra A.3 Matrices on page 441 "If you know what a prticular linear transformation does to a set of basis vectors, you can easily figure out what it does on any ...
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### Spectral functions in quantum mechanics

I'm a math student and a totally newcomer to quantum mechanics and I'm trying to teach myself this subject by studying Faddeev and Yakubovski's Lectures on Quantum Mechanics for Mathematics Students. ...
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I the field of the harmonic oscillator and ladder operators I am trying to solve exercise 2.17 from Sakurai and want to proof the following relation $$\langle x^{2n} \rangle = (2n - 1)!! \langle x^... 1answer 108 views ### What is the Quantum Mechanical Operator for Electric Potential? I understand that charge and electric potential are conjugate observables in QM. See https://en.wikipedia.org/wiki/Conjugate_variables The quantum mechanical operator for charge, q, is simply equal ... 1answer 74 views ### why we dont have “direct” velocity operator just as p? ( as use p space not v? ) in quantum? why there is no direct velocity operator on quantum mechanic while there is for mumentum ( p_{x}=d/dx ) Also why use mumentum space not velocity ? 1answer 105 views ### What is the origin of the quantum operators for p and E? [closed] It is always stated the quantum operators for p and E are the ones we´re familiar with (the operator for energy, H=i\hbar\frac{\partial}{\partial t} and the momentum operator, \mathbf{p}=-i\hbar\... 1answer 51 views ### Orbital angular momentum eigenstates in the |\mathbf{r}\rangle representation Consider the orbital angular momentum operators L^2 and L_z. In the |\mathbf{r}\rangle representation using spherical coordinates those operators actions are given by$$L^2\varphi(\mathbf{r})=-\...
This question has been bothering me for a while now: can one reconstruct an arbitrary (normalizable) function $\phi(\mathbf r)$ in $\mathbb R^3$, with only the discrete set of Hydrogen wavefunctions (...
If $\hat{p}$ acts on position eigenstate, it is $$\tag{1}\hat{p}\left|x\right\rangle=+i\hbar\frac{\partial }{\partial x}\left|x\right\rangle .$$ But in general \tag{2}\hat{p} = -i\hbar \frac{\...