# 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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### Simplify exponential of operators

I got a term similar to the following one $\mathrm{Op}=\exp{\left(-i(\hat{A}+c_1\hat{B}+c_2\hat{C})\right)}\exp{\left(i(\hat{A}+c_1\hat{B}+c_1\hat{C})\right)}$. Does anyone got an idea how to ...
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### Does angular momentum of hydrogen atom imply motion of electron around the nucleus?

Does the non-zero orbital angular momentum (or z-component of angular momentum) of a stationary state of hydrogen atom imply motion of electron (or at least the probability density $|\Psi|^2$) around ...
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### Express state as eigenkets

This is very basic but I just suddenly got confused. Any state can be expressed as complete set of eigenkets with discrete eigenvalues: $$|P\rangle = \sum^n c_n |p_n\rangle$$ I understand the above. ...
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### Trouble understanding Nielsen & Chuang exercise

I am probably just stuck on something very simple, but I'm having trouble understanding a premise of Exercise 10.40 in Nielsen & Chuang. The full details of the exercise are not important for my ...
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### Commutation Relation between Annihilation & Creation Operators and Ascending & Descending Operators

I am currently working on a QD-Cavity system. After the point Heisenberg Equation of motion is obtained from corresponding Hamiltonian of the system, in order to find the expression for bosonic ...
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### Why isn't there a Time Operator in Quantum Mechanics? [duplicate]

I was wondering about a scenario where you subject a quantum particle to an intense gravitation field. Why can't we apply a sort of time operator to the particle to see how time changes for the ...
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### How to construct Hermitian(quantum) operator from a physical experiment?

Suppose I want to study a quantum mechanical quantity of a single particle. I have designed an appropriate apparatus, accuracy of which is limited by relevant laws of quantum theory. I have obtained a ...
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### How to find the corresponding Hamiltonian in quantum, if Hamiltonian in classical mechanics is given? [closed]

Hamiltonian in classical mechanics is $$H=wxp$$ $x=$ position, $p=$ momentum coordinate. Find the corresponding Hamiltonian in quantum mechanics!
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### Invariance of State Vector under Two Operations

I am trying to understand why if you measure one non degenerate operator you get a new state w1v let's say with w1 eigenvalue, then let's say u measure a new operator that has degenerate eigenvalue v ...
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### Is there an angular velocity operator in quantum mechanics?

In classical mechanics we can write as velocity of a rotating object $\vec{v} = \vec{\omega} \times \vec{r}$ or in analogy the momentum $\vec{p} = m (\vec{\omega} \times \vec{r})$ using the angular ...
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### In quantum mechanics, how exactly do we associate Hermitian operators to classical observables? [duplicate]

In a first course on quantum mechanics, everybody learns some version of the following statement: Postulate: To every classical observable $A$ of a physical system, there corresponds a Hermitian ...
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### Euler-Lagrange Equation in Quantum Field Theory

The quantum fields are operator valued distributions. In some sloppy books like Peskin and Schroeder the Euler-Lagrange equation are used to get the equations of motion. What does it mean to take a ...
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### Expectation value of an Observable and Eigenstates

I am learning about Quantum Mechanics at the moment and I was wondering about Eigenfunctions and Observables. The question I would like to ask is, If a wavefunction is not an eigenstate of an ...
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### Why hermitian, after all? [duplicate]

This question is going to look a lot like a duplicate, but I've read dozens of related posts and they don't touch the subject. Here we go. Why are observables represented by hermitian operators? ...
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### Random operator in heisenberg/schrödinger picture (heisenberg's equation of motion) [closed]

Consider a system whose hamiltonian isn't explicitly dependent on time. Let A be the operator for the eigenvalue a in the Schrödinger picture and $A_H=U^\dagger A U$ the corresponding operator in the ...
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### Properties of spectrum of a self-adjoint operator on a separable Hilbert space

So, if I understand it correctly, the spectrum of a self-adjoint operator on a Hilbert space $H$ consists of two parts: $\newcommand{\ket}[1]{\,\lvert{#1}\rangle} \newcommand{\op}[1]{\hat{#1}}$ ...
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### How to form the matrix representation of $|O|^3$

I'm interested in getting the matrix representation of the absolute value of an operator. I know the matrix representation of the operator $O$. Now how do I take its absolute value?
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### Functional Analysis for Quantum Mechnanics [duplicate]

I have completed three sequences of courses in QM, and I'm very much eager to to do the functional analysis of QM on my own in my spare time. Can someone suggest some books? I like books with ...
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### Derivation involving finite unitary transformation [closed]

Hi I just want to confirm a short derivation involving a particular finite unitary transformation which is important in QM. My working is as follows: Given the finite unitary transformation defined ...
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### Heisenberg EOM for $\langle x \rangle$ in momentum eigenstate - where is my error?

Equation of motion for expectation value of a quantum particle in a momentum eigenstate: $$\frac{d}{dt} \langle x \rangle = \frac{1}{i h} \langle [x,H] \rangle$$ and since it's in a momentum ...
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### Question about Eigenvalues of Hermetian Operators Being Real Numbers

I'm still slogging through Quantum Mechanics: The Theoretical Minimum and I've reached another area that baffles me. Susskind uses the following to show that the eigenvalues of Hermitian operators ...
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### Calculating eigenvalues for operator [closed]

Given relation $[a,a^\dagger]=I$. Operator $K$ is defined as $K=a^\dagger a+\lambda a^\dagger+\lambda^* a$. I need to find the eignevalues of operator $K$. How realtion that involves commutator could ...
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### Why is Wick contraction a $c$-number?

It is mentioned in Fetter's Quantum Theory of Many-Particle Systems (in contraction part of section 8 Wick's Theorem), that: contractions are c numbers in the occupation-number Hilbert space, not ...
somewhere I read here: $[A,F(B)]=[A,B]F'(B)$ is used to prove Glauber's formula $\exp(A+B).\exp([A,B]/2)$ I have tried and looked everywhere to try and understand this to no avail. The first is in ...