# Tagged Questions

Applies also to pre-Hilbert spaces, rigged Hilbert spaces, and spaces with negative norm or zero-norm states.

0answers
12 views

### The Wigner angle for two-particle state

Suppose we have the Wigner angle $\theta (\mathbf k, \Lambda)$, which is defined through the Lorentz group transformation $U(\Lambda)$ of one-particle state $|\mathbf k , \sigma\rangle$ ($\sigma$ ...
0answers
37 views

### How to represent the spherical wave by using Fock basis?

Suppose I have two particles with opposite momentum: $$|\psi \rangle_{\mathbf k} = |\mathbf k; -\mathbf k\rangle ,\quad |\mathbf k| = M$$ I want to represent the spherical symmetric distribution of ...
1answer
26 views

1answer
83 views

1answer
81 views

### Single particle tunneling Hamiltonian

In reference to Problem 9, Chapter 2 in Modern Quantum Mechanics by JJ Sakurai, For a single particle tunneling in a 1D double well potential, with position eigenkets $\mid R\rangle$, $\mid L\rangle$....
2answers
144 views

### Is the Noether charge always a Hermitian operator?

Noether's theorem tells us that to every continuous symmetry of the Lagrangian there corresponds a conserved current $j^\mu$. From the time component of this current, we can then define the Noetherian ...
0answers
76 views

### CFT: from States to Operators

I'm having trouble finding the general algorithm for moving from states to operators under the state-operator correspondence in a CFT. Does anyone have any hints as to how one might go about ...
2answers
222 views

### 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 ...
1answer
123 views

1answer
102 views

### Difference between phase space and Hilbert space? [closed]

Why is the phase space of classical mechanics not a vector space, but Hilbert space of QM is?
3answers
84 views

### 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 ...
0answers
38 views

### Why is the inner product of position eigenstates not normalised? [duplicate]

I have read that $$<{\bf r}|{\bf r}'> = δ({\bf r}-{\bf r}').$$ I don't understand how this is correct, I want to say it is equal to 1 or 0, rather than an unnormalised delta function. Clearly ...
0answers
91 views

### Rotations in Bloch Sphere about an arbitrary axis

I am trying to understand the following statement. "Suppose a single qubit has a state represented by the Bloch vector $\vec{\lambda}$. Then the effect of the rotation $R_{\hat{n}}(\theta)$ on the ...
4answers
198 views

### The Theoretical Minimum: Confusion Over Susskind's Reasoning for mutually orthogonal states

There's a better title for this question but my brain is so fried I can't come up with one. Important Note: I am a layman, and my understanding of the mathematical concepts of quantum mechanics is ...
2answers
241 views

### Differences between eigenstates, bound states and stationary states [closed]

I am not very clear about the differences between eigenstates, bound states and stationary states.
2answers
118 views

### 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 ...
1answer
76 views

### Can the quantum mechanical current density be imaginary?

I am dealing with a situation where I get an imaginary transmission current density. Is this possible? Does it imply a zero transmission probability?
1answer
88 views

### 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. ...
1answer
44 views

### Is it necessary to prove the existence of an operator representing symmetry on Hilbert space?

Is there any need to prove the existence of an operator $U$ which represents the action of symmetry transformation on rays in Hilbert space? Or is it enough just to prove that it is unitary and linear ...
1answer
47 views

0answers
49 views