Questions tagged [quantum-states]
The quantum-states tag has no usage guidance.
0
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0answers
35 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)...
0
votes
1answer
20 views
Is mode and orthonormal set of a particle the same thing? [on hold]
Let's say we have a particle $A$ belongs to Hilbert space $H_A$.
The complete orthonormal set of a particle is $\sum_{n=1}^{\infty}|\phi_n \rangle$ belonging to Hilbert space $H_A$.
Now if we write ...
1
vote
1answer
84 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 ...
7
votes
4answers
491 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
60 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 $s$'
$$\vert \psi \rangle = \frac{1}{(\pi^2s^...
0
votes
1answer
41 views
Systems with a finite number of linearly independent states
I am studying systems that admit only a finite number of linearly independent states. In such a case, $|S(t)>$ lives in a N-dimensional vector space and can be represented by a column of N ...
0
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0answers
27 views
Conditions for a separable state to be a CPB-state
A bipartite quantum state $\rho$ is called a CPB(Complete Product Basis)-state if its eigenvectors can be expressed as product state (a pure state of the form of $|\phi\rangle \otimes |\psi\rangle$). (...
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0answers
35 views
Why do the matrix elements of an operator correspond to the Fourier components of the observable in Heisenberg's Matrix Mechanics?
It is well-known that Heisenberg $a$ began developing his Matrix Mechanics by creating matrix components
$$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}$$...
0
votes
0answers
45 views
Superstate vs superposition
Is superstate the phase space of a superposition that includes subsets? It seems like superstate is not used as a word that often, and usually seems to be a synonym for superposition.
Can anyone give ...
0
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1answer
35 views
How to write down the state after a measurement if the result was not recorded?
I measure the spin of an unknown qubit in the computational basis but I do not record what the outcome of the measurement was. How should I now describe the state?
If it is described as a maximally ...
2
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1answer
66 views
What is the overlap $\langle \phi | 0 \rangle$ for a scalar field?
Consider a massive free real scalar field $\hat{\Phi}$ (with $\mathcal{L}[\Phi] = \partial_{\mu}\Phi\partial^\mu \Phi
- \tfrac{1}{2} m^2 \Phi^2$). I was wondering what is the overlap for the ...
2
votes
1answer
54 views
Can a single-qubit state be nontrivially extended to a non-pure state?
Consider a generic single-qubit state
$$\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.$$
I am interested in ...
0
votes
2answers
124 views
Orthogonal wave functions
I am wondering: can we explain the concept of orthogonality in physics for a beginner (without much math and linear algebra) by saying it simply means that the particle can not exist in two different ...
2
votes
1answer
44 views
Does measurement with unknown outcome transform a pure superposition state into a mixed state?
$\def\+{\!\!\kern0.08333em}$
Say I have a spin-1/2 particle in a general, pure superposition state
$$
|\psi\rangle=\alpha|\+\uparrow\rangle+\beta|\+\downarrow\rangle,
$$
or equivalently
$$
\rho=(\...
-4
votes
1answer
42 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
70 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
114 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
40 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
27 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
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2answers
203 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?
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0answers
16 views
over all phase has no effect on a quantum state
It is said that the over all phase does not effects the quantum state, only relative phase changes the state.how would we shown it on bloch sphere
4
votes
1answer
79 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
227 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
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0answers
49 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
70 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
31 views
Are tensored qubits commutative?
I am given a solution to a problem, saying that
$$
|\psi\rangle_{ABC} = \frac{1}{\sqrt{2}}(|0\rangle_A \otimes |1\rangle_C + |1\rangle_A \otimes |0\rangle_C) \otimes |+\rangle_B
$$
$$
= \frac{1}{2}(...
-1
votes
1answer
130 views
Is $e^{-2x}\sinh x$ an acceptable state wavefunction?
I have the following function in the range $(0, \infty)$:
$$\psi(x)=e^{-2x}\sinh x$$
I would like to know if it is acceptable as a wavefunction. At $x = \infty$, we have $e^{-2x} = 0$ ...
2
votes
5answers
158 views
Why do we use vectors in quantum mechanics?
I've been trying to make my understanding of quantum mechanics more mathematically rigorous, but I'm struggling a bit with the lack of intuition behind the fact that we represent quantum states with ...
4
votes
1answer
71 views
What is the inner product between a position ket and a two-state (or multi-state) ket?
I am recently studying the two-state system in quantum mechanics.
As I learned, in the Hilbert space of a spinless particle, the relation between a scalar function and a ket state is satisfied as,
$$...
0
votes
0answers
53 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. ...
1
vote
3answers
150 views
Why is it not possible to describe a mixed quantum state by a Hilbert space vector?
I read (for instance in Landau/Lifshitz III) that if I know the wave function of a quantum state, I have the maximal information of the state available, in different words, the description of the ...
0
votes
0answers
6 views
Translating between classical treatment of non-autonomous systems and time evolution in quantum mechanics
When I read an introduction to (classical) dynamical systems, the system was considered in a phase space, and the state of the system evolving in phase space. For a non-autonomous system, an ...
7
votes
1answer
139 views
Characterisation of the generalised Bloch sphere in spherical coordinates
I'm so confused by the following definition in the "Quantum Error Correction" by Lidar and Brun that not even sure how to formulate the question properly.
Let $\mathbf n$ denote a unit vector, i.e.,...
1
vote
1answer
50 views
Orthogonality of Scattering states
The scattering states solution ($E>V_0$) to the time independent Schrodinger equation for a finite square barrier ($V_0$ ) in an otherwise free region has the form:
$$\psi(x)=\begin{cases}e^{i k x}...
0
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0answers
22 views
Energy level in harmonic oscillator [duplicate]
ground state is always non degenrate in harmonic oscillator in quantum state, why?
1
vote
0answers
52 views
Is the space of gauge invariant states a Hilbert space?
In a theory with a gauge symmetry, as I understand it, the gauge symmetry is not a symmetry of a system, but rather its a redundancy in description. The procedure goes like this start with some ...
0
votes
0answers
39 views
What does it mean for a quantum state to have even parity?
Parity is a spacial reflection of coordinates. I understand that much. When it comes to quantum states though I'm a bit confused. Can someone explain it to me in layman's terms?
1
vote
1answer
84 views
In Algebraic QFT, is the state observer dependent?
In the usual approach to QFT presented e.g., in Weinberg's book, the state of a system is dependent on the observer. Quoting this book, in page 109 we have:
Notice how this definition is framed. To ...
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vote
0answers
55 views
Dimensions and complex vector space
I am getting rather confused by the dimensions of the Hilbert space in which a state $\psi$ lives, and with regards to the distinction between the Hilbert space and projective Hilbert Space.
Consider ...
4
votes
1answer
103 views
Definition of state of a quantum system
In QM, we solve for the eigen kets of the Hamiltonian operator $\hat{H}$ and say that the state of my system lies in a linear superposition of these eigenstates $\{|n\rangle\}$ as the relation implies ...
1
vote
1answer
47 views
Transition from an initial/final position state to the ground state in the path integral
I am reading chapter 6 of M.Srednicki's book. On page 47 he argues why it is possible to choose for the initial/final state the ground state instead of a position state. Actually I don't understand ...
2
votes
1answer
35 views
How can the symmetry of the quantum state fidelity be shown directly?
Consider the quantum state fidelity $F(\rho,\sigma)$ defined as (I will use the notation used in Nielsen & Chuang here):
$$
F(\rho,\sigma) \equiv
\operatorname{Tr}\sqrt{\rho^{1/2}\sigma\rho^{1/2}} ...
0
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0answers
69 views
Obtaining the number of quanta for a system of harmonic oscillators
So I need to find the entropy of a system made up of two harmonic oscillators having natural frequency $\omega_0$ and $2\omega_0$. The system is said to have a total energy of $E=(n+\frac12)\hbar\...
1
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0answers
48 views
Operational definition of quantum states [closed]
I came across a basic textbook problem. I am clear with the math, but I am not clear with how it is connected with experimental facts.Before stating the actual problem.
Let me quote Karl Krauss from ...
-1
votes
1answer
115 views
What do Quantum Physicists mean by this? [closed]
When it comes to the mystical field of quantum physics, I am often told that a particle system, such as an electron, can exist in many states at once and is thus able to occupy many different volumes ...
1
vote
2answers
145 views
Difference between the energy eigenstates and the eigenstates of other physical variables
I am having difficulties understanding the difference between the energy eigenstates and the eigenstates of other physical variables. I was told that if a system is an energy eigenstate at $t = 0$ ...
0
votes
0answers
47 views
Fermi's golden rule - possible final states
While reading about Fermi's Golden Rule on Wikipedia, I found that claim:
"If $H'$ is time-independent, the system goes only into those states in the continuum that have the same energy as the ...
1
vote
1answer
71 views
Is *Conservation of Distinction* a true conservation law in mainstream physics?
Both Leonard Susskind and Francis Heylighen have written about the Conservation of Distinction but it seems Susskind more closely connects this (law?) with unitarity in quantum mechanics. Heylighen ...
1
vote
1answer
133 views
Global phases and indistinguishable quantum states, mathematical understanding
Im trying to mathematically understand this: "All four states are mathematically identical, up to a global phase, and global phases do not distinguish quantum states. "
$$ \displaystyle \frac{|0\...
