A quantum state is a mathematical entity (abstract geometrical or specific algebraic function) that provides a probability distribution for the outcomes of each possible measurement on a system.
Questions tagged [quantum-states]
603 questions
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How should we think about Spherical Harmonics?
Studying Quantum Mechanics I only thought about Spherical Harmonics $Y_{l,m}(\theta , \phi)$:
$$Y_{l,m}(\theta , \phi)=N_{l,m}P_{l,m}(\theta)e^{im\phi}$$
as the simultaneous eigenfunctions of $L_z$ and $L^2$.
But then I stumbled on these two…
Noumeno
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Why can't every quantum state be expressed as a density matrix/operator?
It was my previous impression that all quantum states in a Hilbert space can be represented using density matrices† and that's already the most general formulation of a quantum state. Then I came across yuggib's comment here:
Everything would be so…
user199113
14
votes
4 answers
What is the difference between a Hilbert space of state vectors and a Hilbert space of square integrable wave functions?
I'm taking a course on quantum mechanics and I'm getting to the part where some of the mathematical foundations are being formulated more rigorously. However when it comes to Hilbert spaces, I'm somewhat confused.
The way I understand it is as…
Milan
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Can the wavefunction be inferred from the expectation values of operators?
Preface
This question is motivated by $C^*$ type treatments of quantum mechanics where operators (Basically an operator is an object that has a spectrum) are treated as fundamental and states are functionals on those operators that map operators to…
Jagerber48
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Path integral derivation of the state-operator correspondence in a CFT
Below, I paraphrase the path integral derivation of the state-operator correspondence in chapter 4 of David Tong's string theory notes (see pdf here). This is my interpretation of the text in that pdf, so please correct me if I'm wrong
He starts…
Prahar
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What does Hartle's derivation of the Born rule actually amount to?
There have been many questions asked here on the topic of whether the Born rule can be derived from the rest of the axioms of quantum mechanics. See, for example, this and links therein. However, I want to ask about a specific derivation of the Born…
user87745
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votes
6 answers
In quantum mechanics, is $|\psi\rangle$ equal to $\psi(x)$?
So I'm going through my notes and I think I've confused myself. We often imply
$$
|\psi\rangle \to \psi(x)\\
\langle\psi| \to \psi(x)^*
$$
for instance when we talk about eigenvalue equations we interpret
$$
\hat{H}|\psi\rangle…
user7971589
- 145
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How is a bound state defined in quantum mechanics?
How is a bound state defined in quantum mechanics for states which are not eigenstates of the Hamiltonian i.e. which do not have definite energies? Can a superposition state like…
SRS
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Why do we need mixed states in quantum mechanics?
I am trying to understand the necessity of density matrices and the notion of "mixed states" in quantum mechanics (I read all the other posts about this, I promise).
As far as I understand, one could motivate these notions as follows:
Let $H_1$ and…
Bipolar Minds
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What do the quantum fields represent, mathematically?
I am looking for insight on quantum field theory, and more precisely, I am interested in having a low-detailed idea of what a quantum field theory is about; moreover, I should say hat I am a mathematician with little physical background.
I found…
Plop
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What does it mean to apply an operator to a state?
Let's say I have an operator $\hat{A}$ and a state $|\psi\rangle$. What exactly is the state $\hat{A}|\psi\rangle$? Is it just another different state that I am describing using my $\hat{A}$ and $|\psi\rangle$? For example, if
$$\hat{A} \doteqdot…
Ignacio
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What is the minimum number of separable pure states needed to decompose arbitrary separable states?
Consider a separable state $\rho$ living in a tensor product space $\mathcal H\otimes\mathcal H'$, with $\mathcal H$ and $\mathcal H'$ of dimensions $D$ and $D'$, respectively.
If $\rho$ is separable, then it is by definition possible to write it as…
glS
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The definition of Gaussian State
Could you clarify to me what is a Gaussian state? I know what is a Gaussian function and Gaussian distribution, but I don't know how to respond to other when they ask me to provide the definition of a Gaussian state.
Thank you.
TBBT
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votes
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Why do we choose the Dirac delta function as the eigenstate of position operator?
When we try to find the eigenstates of the position operator, we get that the product of (x-y) and the eigenstate must be zero. It is obvious then that for x different than y, the eigenstate must be zero.
Now for x equal to y, how do we know that…
MTYS
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Can Schrödinger's cat be revived?
According to Quantum Mechanics, Schrödinger’s cat is in a superposition state of $\frac{1}{\sqrt{2}}(\left|A\right> + \left|D\right>)$, where $\left|A\right>$ and $\left|D\right>$ correspond to alive and dead state respectively. An external observer…
wei
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