Questions tagged [quantum-states]
The quantum-states tag has no usage guidance.
0
votes
1answer
46 views
Eigenstates of position in Schrödinger picture
Hallo I'm trying to understand the concept of representation in the position space.
I read that $|x\rangle$ are the eigenstates of the position operator, but I think this states should evolve in time ...
0
votes
2answers
40 views
About superposition of states
In quantum computing, we can always create an arbitrary superposition of states by rotation of $|0\rangle$ state for one qubit. This raises a question: for arbitrary superposition of states, is there ...
1
vote
1answer
62 views
Does $[L_z,H] = 0$ imply the state is also an Eigenstate of $H$ is also an eigenstate of $L_z$?
Given that the Hamiltonian $\mathcal{H}$ is rotationally invariant then we know $[L_z,\mathcal{H}] = 0$. Does that imply that an eigenstate of H is also an eigenstate of $\mathcal{H}$?
More ...
2
votes
1answer
139 views
What does $|$ mean in the Schrödinger Equation?
I saw the $|$ symbol in the Schrödinger Equation $$i\hbar\frac{\partial}{\partial{t}}|\Psi(r,t)\rangle=\hat{H}|\Psi(r,t)\rangle$$ But I don't know what the $|$ means.
What does $|$ mean in the ...
0
votes
2answers
62 views
Relation between giving the form of an operator in a given representation, and bra ket notation
So I understand that kets are abstract objects that are the elemnets of a Hilberts space. Say $|\psi \rangle$.
We can write this ket in a position representation $\langle r|\psi \rangle = \psi(r)$, ...
-3
votes
0answers
41 views
Doubt regarding the angular momentum in quantum mechanics
What does $L^2|l,m\rangle$ indicate?
Can anyone specify the 2 states in a ket vector of angular momentum $|l,m\rangle$?
$$L^2|l,m\rangle=\hbar^2(l+1)l|l,m\rangle$$
and how to differentiate between $\...
2
votes
4answers
110 views
Why do wavefunctions for stationary states include $e^{-iEt/\hbar}$? [duplicate]
Stationary states are separable solutions with $\Psi(x, t)=\psi(x)e^{-iEt/\hbar}$. But why is that there? Griffiths (Section 2.1 Stationary states, equation 2.8) says that observables for these states ...
0
votes
0answers
25 views
Why do the matrix elements of an operator correspond to the Fourier components of the observable in Heisenberg's Matrix Mechanics?
It is well-known that Heisenberg $a$ began developing his Matrix Mechanics by creating matrix components
$$A(n,n-a,t)=A(n,n-a)e^{i\omega(n,n-a)t}$$
or
$$A_{nm}(t)=A_{nm}e^{\frac{i}{\hbar}\omega(nm)t}$$...
0
votes
0answers
22 views
Need help understanding weird definition of pure states [duplicate]
So in many sources I have read that
A pure state contains only one element, since the only entry on the
density matrix will be 1.
But what about superpositions?...
8
votes
3answers
201 views
What exactly is $\langle x |$?
It's a linear functional, but what exactly does it do? It maps a wavefunction $|\psi \rangle$ to an element of $\mathbb C$, but what.. exactly does that mean? I know heuristically it maps $\psi$ to ...
1
vote
1answer
68 views
Description of quantum state of entangled photons after polarizer
I'm wondering if anyone can help me understand how a polarizer changes the quantum state of two polarization-entangled photons. I haven't found a clear description in the literature.
Suppose you have ...
1
vote
0answers
30 views
Fidelity and approximately unentangled states
It is well known that fidelity distributes over product states, i.e.
$$F(\rho \otimes \rho, \tau \otimes \tau) = F(\rho, \tau) \cdot F(\rho, \tau),$$
and more generally,
$$F(\rho^{\otimes N}, \tau^{...
0
votes
1answer
44 views
Probability of measuring Energy [closed]
I have done the first part of the question, but in (b) and (c) are struggling me .
I second part :
My tutor wrote :
$$ P(req.) = \frac{|\int \phi_E^*(x)*\psi(x,t) dx |^2}{|\int\: \psi^*(x,t)*\...
1
vote
1answer
51 views
How to use tensors and operators
I have some problem understanding how to use tensors. Let's say in Quantum Optics if I have the state in mode $b$ (where I can have two possible modes $a$ and $b$)
$$|1_b\rangle = |0_a\rangle \otimes|...
3
votes
2answers
91 views
What happens to a wavefunction upon measurement when there's degeneracy?
I'll use a hydrogen atom as an example. A hydrogen atom has multiple energy eigenstates for all but one of its energy levels. Suppose I measure a hydrogen atom to have an energy $E_n$ where $n > 1$....
3
votes
1answer
76 views
Why must I solve the de Broglie relationship in a single dimension instead of all three?
Context: a particle of mass $m$ can move in 3D and is trapped inside of a sphere of radius $R$ and impenetrable walls (in a more mathematical sense, the potential energy is 0 inside of the sphere and $...
1
vote
2answers
66 views
Tensor product of kets and bras
My question is about tensor products. I have learned that the tensor product between two operators is, for example, $A{\otimes}B$. Suppose we have a system $A$ and a system B. Why we can write the bra ...
0
votes
2answers
67 views
A confusion about why can't a statistical mixture be modelled as a superposition of pure states?
I have read Cohen's book, and various posts in this site; however, I'm still not convinced why we can't model a statistical mixture as a superpositions of pure states ?
For example, consider the ...
1
vote
1answer
46 views
Entanglement in quantum physics [duplicate]
Mathematically what is the difference between pure separable state and entangled state ?
Can anyone explain with equations?
0
votes
0answers
28 views
Mathematical analysis of recombining streams in a Stern-Gerlach experiment
My quantum mechanics textbook skips some steps in its mathematical analysis of a Stern-Gerlach experiment, and I am having trouble filling in the blanks.
The experiment sends a streams of electrons ...
2
votes
0answers
48 views
What does a “pure” state mean in QM? [duplicate]
Question:
In Quantum Mechanics, people use the word "pure state" for some states; however, what do they mean exactly ?
Thoughts:
I mean, a state is a vector in our vector (Hilbert) space, so in that ...
1
vote
2answers
70 views
Energy Expectation Value = 0 - Meaning?
I've solved an exercise of a given quantum system with 3 given states. We had to find the energy expectation value, when we put the system in the "second starting quantum state".
So I did the ...
0
votes
0answers
45 views
Difference between pure and thermal states
As far as I know by inserting a harmonic potential $V(x) = \frac{1}{2}m \omega x^2$ into the time-independent schrödinger equation I can obtain the wave-functions eigenstates and eigenvalues (energies)...
1
vote
1answer
91 views
How to “resolve a state” with respect to a spacelike hypersurface in Minkowski Spacetime QFT?
Consider usual free QFT in Minkowski spacetime. For simplicity let us consider a real scalar field $\phi$. Usually quantization is performed with respect to one inertial reference frame. This is is ...
8
votes
4answers
570 views
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 ...
1
vote
1answer
71 views
No-S-$B^+$ Theorem like Results
Classification of multipartite quantum state is an interesting topic in quantum information and there have been many accomplishments in the field. For example, according to the result of Thapliyal, ...
-1
votes
1answer
63 views
Gaussian State Spread [closed]
A measurement device which can be represented by a 1D quantum system (with canonical observables $X$ and $P$) 'is prepared in a Gaussian state with spread $s$'
$$\vert \psi \rangle = \frac{1}{(\pi^2s^...
0
votes
1answer
43 views
Systems with a finite number of linearly independent states
I am studying systems that admit only a finite number of linearly independent states. In such a case, $|S(t)>$ lives in a N-dimensional vector space and can be represented by a column of N ...
0
votes
0answers
28 views
Conditions for a separable state to be a CPB-state
A bipartite quantum state $\rho$ is called a CPB(Complete Product Basis)-state if its eigenvectors can be expressed as product state (a pure state of the form of $|\phi\rangle \otimes |\psi\rangle$). (...
0
votes
0answers
55 views
Superstate vs superposition
Is superstate the phase space of a superposition that includes subsets? It seems like superstate is not used as a word that often, and usually seems to be a synonym for superposition.
Can anyone give ...
0
votes
1answer
36 views
How to write down the state after a measurement if the result was not recorded?
I measure the spin of an unknown qubit in the computational basis but I do not record what the outcome of the measurement was. How should I now describe the state?
If it is described as a maximally ...
2
votes
1answer
70 views
What is the overlap $\langle \phi | 0 \rangle$ for a scalar field?
Consider a massive free real scalar field $\hat{\Phi}$ (with $\mathcal{L}[\Phi] = \partial_{\mu}\Phi\partial^\mu \Phi
- \tfrac{1}{2} m^2 \Phi^2$). I was wondering what is the overlap for the ...
2
votes
1answer
58 views
Can a single-qubit state be nontrivially extended to a non-pure state?
Consider a generic single-qubit state
$$\rho=\lambda_1\lvert \lambda_1\rangle\!\langle \lambda_1\rvert+\lambda_2\lvert \lambda_2\rangle\!\langle \lambda_2\rvert\in\mathcal H_S.$$
I am interested in ...
0
votes
2answers
231 views
Orthogonal wave functions
I am wondering: can we explain the concept of orthogonality in physics for a beginner (without much math and linear algebra) by saying it simply means that the particle can not exist in two different ...
2
votes
1answer
49 views
Does measurement with unknown outcome transform a pure superposition state into a mixed state?
$\def\+{\!\!\kern0.08333em}$
Say I have a spin-1/2 particle in a general, pure superposition state
$$
|\psi\rangle=\alpha|\+\uparrow\rangle+\beta|\+\downarrow\rangle,
$$
or equivalently
$$
\rho=(\...
-4
votes
1answer
44 views
In a quantum state, Maximum how many protons & neutrons can exist?
This is in reference to the statement I have read in a book i.e., " each quantum state can contain at the most two protons (with opposite spin) & two neutrons (again with opposite spin)".
So what ...
2
votes
1answer
114 views
Is partial trace the inverse operation of Kronecker product?
Computer science student here, who is interested in quantum information theory.
Suppose I have these pure states:
\begin{bmatrix}1&0\\0&0\end{bmatrix} and
\begin{bmatrix}0&0\\0&1\end{...
-3
votes
4answers
120 views
What is the difference between $\vert-\rangle$ and $\vert+\rangle$?
I understand that a Qubit can be represented in the form of $$\vert\psi\rangle=\alpha \vert0\rangle+\beta\vert1\rangle$$ where $\alpha$ and $\beta$ are complex numbers and the $\alpha^2$ and $\beta^2$ ...
0
votes
1answer
42 views
What happens to a particle in a well if the well is made bigger? [duplicate]
Let's say we have a particle in an infinite well, and let's also say it is in the ground state. Now we make the well bigger by very quickly moving one of the boundaries of the well.
How do we ...
2
votes
1answer
29 views
How do we know which term to attach a phase factor to in a state equation?
I need to find the state of a particle in a one-dimesional harmonic oscillator where a measurement of the energy yields the values $\hbar\omega\over 2$ or $3\omega\hbar\over 2$, each with a ...
4
votes
2answers
219 views
Why do we describe physical systems in Hilbert space?
In quantum mechanics we study physical systems associated with a Hilbert space. Why do we need a Hilbert space to describe the state of a system?
4
votes
1answer
103 views
What is the difference between a state vector and a basis vector in Quantum mechanics?
I searched about the difference between state vector and basis vector in Quantum mechanics but couldn't find any clear explanation. Can someone please give a simple and clear explanation of this?
8
votes
6answers
257 views
In quantum mechanics, is $|\psi\rangle$ equal to $\psi(x)$?
So I'm going through my notes and I think I've confused myself. We often imply
$$
|\psi\rangle \to \psi(x)\\
\langle\psi| \to \psi(x)^*
$$
for instance when we talk about eigenvalue equations we ...
1
vote
1answer
68 views
Classical correlations in bipartite entangled mixed state
I have recently asked somewhat related question and got very illuminating answer. After some thinking however I have realized that (at least) one more point is unclear to me:
How can we check ...
0
votes
1answer
87 views
How to undo or reverse a Kronecker product (tensor product) in QuTiP? [duplicate]
Let's say I have a qubit. A qubit is described by the two basis state
$$|0\rangle=
\begin{pmatrix}
1\\0
\end{pmatrix}
\quad\text{and}\quad
\ |1\rangle=
\begin{pmatrix}
0\\1
\end{pmatrix}.
$$
So a ...
1
vote
1answer
33 views
Are tensored qubits commutative?
I am given a solution to a problem, saying that
$$
|\psi\rangle_{ABC} = \frac{1}{\sqrt{2}}(|0\rangle_A \otimes |1\rangle_C + |1\rangle_A \otimes |0\rangle_C) \otimes |+\rangle_B
$$
$$
= \frac{1}{2}(...
-1
votes
1answer
179 views
Is $e^{-2x}\sinh x$ an acceptable state wavefunction?
I have the following function in the range $(0, \infty)$:
$$\psi(x)=e^{-2x}\sinh x$$
I would like to know if it is acceptable as a wavefunction. At $x = \infty$, we have $e^{-2x} = 0$ ...
2
votes
5answers
204 views
Why do we use vectors in quantum mechanics?
I've been trying to make my understanding of quantum mechanics more mathematically rigorous, but I'm struggling a bit with the lack of intuition behind the fact that we represent quantum states with ...
4
votes
1answer
108 views
What is the inner product between a position ket and a two-state (or multi-state) ket?
I am recently studying the two-state system in quantum mechanics.
As I learned, in the Hilbert space of a spinless particle, the relation between a scalar function and a ket state is satisfied as,
$$...
0
votes
0answers
67 views
Difference between Coherence Transfer, Polarization Transfer & Population transfer
Previously I asked some questions on quantum coherence and the answer helped me to clear the concept. I did some more literature review to understand the basic facts in relation to density matrix. ...
