Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with hilbert-space
Search options not deleted
user 326183
This tag is for questions relating to Hilbert Space, a vector space equipped with an inner product, an operation that allows defining lengths and angles, and the space is complete. It arises naturally and frequently in mathematics and physics, typically as infinite-dimensional function spaces having the property that it is complete. Applies also to pre-Hilbert spaces, rigged Hilbert spaces, and spaces with negative norm or zero-norm states.
5
votes
2
answers
879
views
Wave functions as being square-integrable vs. normalizable
I am a physics undergraduate. I am working in the world of textbook (non-relativistic) Quantum Mechanics. Say we have a wave function $\Psi(x,t)$. Must $\Psi(x,t)$ be square-integrable or normalizable …
- 3,295
3
votes
Is maximal entanglement basis independent?
Let $\mathcal{H}$ with dimension $\dim \mathcal{H} = 2^n$ where $n \in \mathbb{N}$ be a Hilbert space describing your system of interest. This could be a Hilbert space for a system of $n$ qubits, for …
- 3,295
1
vote
3
answers
657
views
Eigenstates of time dependent Hamiltonians
I am trying to figure out how to make sense of a time dependent Hamiltonian. In the Schrödinger picture, the one dimensional Hamiltonian is written:
$$\hat{H} = -\frac{\hbar^2}{2m}\frac{\partial^2}{\p …
- 3,295
1
vote
Question regarding Hermitian property of Operators
It looks like you are mixing notations. Let us clarify a few things.
Let $\mathcal{H}$ be our Hilbert space. Let $\hat{A}$ be an operator over our Hilbert space, i.e., $\hat{A}: \mathcal{H} \rightarro …
- 3,295
3
votes
Accepted
On the irrelevance of the global phase factor
Let us clarify some of the words and concepts you use in your post.
First, a system is represented by a Hilbert space $\mathcal{H}$. A state of that system is represented by a ray associated with a no …
- 3,295
1
vote
What are the necessary conditions for this statement?
By using the notation $\langle . \lvert . \rangle$, you are referring to a complex inner product.
Let $\mathcal{H}$ be a complex vector space. A complex inner product is a map $\langle . \lvert . \ran …
- 3,295
2
votes
Accepted
On an intuitive way of characterizing "the amount of entanglement" in a bipartite system
First, the definition of entanglement.
Let $\mathcal{H} \cong \mathcal{H}_1 \otimes \mathcal{H}_2$ be your composite Hilbert space (of two particles). A state $\lvert \psi \rangle \in \mathcal{H}$ is …
- 3,295
2
votes
0
answers
93
views
Computing Fubini-Study expectation values over $\mathbb{C}P^n$
In finite-dimensional textbook quantum mechanics, we postulate that states of our system are rays in a Hilbert space $\mathcal{H}$ with dimension $\dim{\mathcal{H}} = n+1$ where $n \in \mathbb{N}$, in …
- 3,295
8
votes
Accepted
What is the Majorana stellar representation?
The Majorana stellar representation is a way to geometrically visualize pure spin-s states. In essence, the Majorana stellar representation 1) establishes a bijection between states of Hilbert space a …
- 3,295
2
votes
0
answers
95
views
Is Sakurai's derivation of the Lippmann-Schwinger equation correct?
I am using Sakurai's Modern Quantum Mechanics 3rd ed. The following is from the beginning of chapter 6.
The defining equation for the $T$-matrix is
$$\langle \vec{k}' \lvert U_I(t, t_0) \lvert \vec{k} …
- 3,295
1
vote
2
answers
119
views
Motivation behind defining mixed states
I am a physics undergraduate. I just read through Sakurai's section 3.4 (3rd ed) on Density Operators and Pure vs. Mixed states.
Are pure states as kets generalized to mixed states as operators in ord …
- 3,295
0
votes
The abstract state of a particle
At a high level, a state of a quantum system is a vector $\lvert \psi \rangle$ of a complex vector space $\mathcal{H}$. If you recall the definition of a vector space, a vector need not be a column of …
- 3,295
5
votes
2
answers
654
views
What is the Majorana stellar representation?
One can geometrically visualize spin-1/2 states using the Bloch sphere. A natural question then is: "Can one geometrically visualize spin-$s$ states using a similar object to the Bloch sphere?" It see …
- 3,295
1
vote
What theorem is behind writing an operator in matrix form as outer products?
As pll04 says in their comment: the spectral theorem for Hermitian operators.
Let $\mathcal{H}$ be a Hilbert space. It is perhaps helpful to note that $\lvert \psi \rangle \in \mathcal{H}$ is simply a …
- 3,295
1
vote
2
answers
347
views
Unitary Time Evolution Operator
I am a physics undergraduate reading through section 2.1 of Sakurai's Modern Quantum Mechanics (3ed). Note that I am dealing with a time independent Hamiltonian.
I have been having a hard time parsing …
- 3,295