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Questions tagged [quantum-states]

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Experimental preparation of an electron plane wave with given momentum in quantum mechanics

Boiling electrons off a hot filament constitutes a preparation providing a mixed ensemble with nearly Maxwellian distribution of momentum eigenstates. To further purify the ensemble, one can let the ...
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2answers
108 views

How is the wave function viewed as the quantum state?

I am not sure how the wave function can be viewed as quantum state. I begin with the eigen-equation $$A|\psi\rangle = a|\psi\rangle$$ If $A$ is a $n$ dimensional matrix with different eigenvalues $...
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106 views

How do you experimentally distinguish $\psi_1 \otimes \psi_2$ and $\psi_2 \otimes \psi_1$?

What I am asking is that $\psi_1 \otimes \psi_2$ and $\psi_2 \otimes \psi_1$ are obviously different states. However, theoretically a measurement can be done that these to states will give two ...
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1answer
86 views

Do pure states actually exist?

Is it possible to ever actually measure something so precisely that it actually collapses to a pure state, or do we really just get arbitrarily close? If a wavefunction never actually collapses to a ...
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3answers
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Difference between eigenstate and basis vector?

My understanding is that any wavefunction can be decomposed into a linear sum of basis vectors, which for momentum are something like sine waves and for position are delta functions. And then ...
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1answer
72 views

Is there a good notation for basis states in quantum mechanics? [closed]

Given a complete set of orthogonal basis states $|e_i\rangle$ one can form any vector $|a\rangle = \sum_i a_i |e_i\rangle$. Is there a standard notation to separate out a basis state from a general ...
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2answers
90 views

Contradiction between aymptotically free particles in QFT and unlocalization

When studying different interactions in any QFT, one always assumes that the IN and OUT states are asymptotically free particles with definite momenta. For example, one assumes that an electron and a ...
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1answer
73 views

How to determine initial quantum state? [closed]

A particle in an infinite square well has its initial wave function an even mixture of the first two stationary states: $$\psi(x,0)=A(\psi_1(x)+\psi_2(x)) $$ As you may know, for $\psi(x,t)$ we ...
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1answer
45 views

Determining the state of a system

My textbook says: "To determine the state of a system at a given instant, it suffices to perform on the system a set of measurements corresponding to a complete set of commuting observables (CSCO)" ...
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0answers
38 views

Gaussian unitary transformations

My reference (Quantum Continuous Variables / Serafini, Alessio) says "It should be intuitively clear that a unitary transformation sends all Gaussian states into Gaussian states if and only if it ...
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1answer
58 views

What is the implication of overlap between eigenstates of two operators in Quantum Mechanics?

For instance, what does it mean that a certain position eigenstate is also an energy eigenstate? I understand that measurable (Observables) in Quantum mechanics are the operators. Their eigenvalues ...
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1answer
37 views

What is a pseudopure state?

In the paper titled "Experimental Implementation of the Quantum Baker’s Map" by Weinstein et al. (Phys. Rev. Let. 89 (2002)), the author says something like [...] the pseudopure state corresponding ...
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1answer
103 views

Does the Choi-Jamiolkowski isomorphism really establish a connection between kinematics and dynamics?

I understand the mathematical construction of the Choi-Jamiolkowski isomorphism aka channel-state duality . It all makes sense formally, yet I still struggle to grasp its physical (or quantum-...
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A doubt about a naive generalization of inner product in elementary quantum mechanics

A elementary study of Quantum Mechanics, following $[1]$, yields in the realization that the basic algebraic structure are the complex vector spaces $\mathbb{C}^{n}$. Then a contravariant vector (...
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1answer
40 views

Is this a projection of a tensor state?

Take the state $|\Psi\rangle $ living in a product space of space 1 and space 2 with orthonormal bases $\varphi,\phi $ $$|\Psi\rangle=\sum_{i,j}a_ib_j|\varphi_i\rangle\otimes|\phi_j\rangle $$ Is the ...
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Have you ever seen: $\sqrt{\rho_{ee}\rho_{gg}}$-|$\rho_{eg}$|?

The next term appears in my research and it is quite meaningful: $\sqrt{\rho_{ee}\rho_{gg}}$-|$\rho_{eg}$| Where $\rho_{gg}$ and $\rho_{ee}$ are the populations in the excited and ground states, and $...
2
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1answer
106 views

Confusion about mixed states and pure states

Suppose I have a system composed of two subsystems (each is a 2-state system). I understand, that there exist two types of such systems: separable, and entangled. A separable system can be written as $...
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1answer
42 views

In practice, how does one work with the phase states?

The phase states are defined usually by the finite sum $$ |\theta \rangle = (s+1)^{-1/2}\sum_{n=0}^s \exp(i n\theta) |n\rangle, $$ where $\theta = 2\pi k/(s+1)$ and $|n\rangle$ is the $n$-th ...
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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 ...
2
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1answer
56 views

Why can there be more than one electron in an energy level if electrons are fermions?

By the Pauli-Exclusion Principle, no two electrons can be in the same quantum state. So, how can both be in the same energy eigenstate? Atom orbitals certainly have more than one electron per energy ...
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1answer
41 views

Is the Schmidt basis the one minimizing entanglement?

I know, that for a compound system $ |\psi \rangle_{AB} $ we can find the Schmidt basis, which is an unique one. Is it at the same time the basis, in which the two subsystems are minimally entangled? ...
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63 views

Orthogonalizing a Gaussian Basis

Given a discrete Gaussian basis $$G = \{\lvert n\rangle, n \in \mathbb{Z}\},$$ where $$\langle x\rvert n \rangle = \exp\left(\dfrac{-(x-nL)^2}{2}\right),$$ with $L$ fixed. Does there exist a set of ...
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4answers
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How is Pauli's exclusion principle valid for electrons of two hydrogen atoms in ground state, having same spin?

Suppose we have two hydrogen atoms in the ground state with spin of both electrons pointing upwards. Then the two electrons are in the same state. This should be against the exclusion principle. Now ...
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1answer
57 views

Problem with understanding Time Evolution of a Quantum State [closed]

I was given the following task and I'm having some troubles with understanding a few things about it: There is given a system with Orthonormal basis $ |u_1 \rangle , |u_2 \rangle, |u_3 \rangle$ ...
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1answer
99 views

Pauli Exclusion Principle and Quantum States [closed]

We know that two identical fermions cannot be in the same state together because of the Pauli exclusion principle. My questions are: Can two bosons (for example, photons) be arbitrarily close ...
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0answers
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By recombination ion/electron does predominataly the ground level form?

When an electron is near an ion and has small velocity it will be certainly captured and both form an atom. I think that the electron will predominantly release energy dE just the proper quantity ...
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1answer
127 views

How to derive Eq. (6.21) in Srednicki?

I'm reviewing Srednicki's chapter on path integrals and am having trouble understanding how he arrives at formula 6.21: $$\left<0|0\right>_{f,h}= \int \mathcal{D}q \,\mathcal{D}p \, \exp \left[...
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1answer
55 views

How to understand the kernel as a transition amplitude?

Consider the time evolution operator $U(t_f, t_i)$ that controls the evolution of a wave function according to $|\psi(t_f \rangle = U(t_f, t_i) | \psi(t_i) \rangle$. As I understand it, the Born ...
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2answers
132 views

When do the eigenkets of an operator form a(n) (orthogonal) basis for the Hilbert space?

When do the eigenkets of an operator form a(n) (orthogonal) basis for the Hilbert space? Is it always the case when the operator is Hermitian? Does the operator need to be Hermitian?
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2answers
268 views

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 $\left|D\right>$ ...
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0answers
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Is $\langle \phi_m|\dot{\phi}_n\rangle$ assumed real in electronic excitation theory?

I'm studying a topic of the Nikitin's book (see pages 101 and 105) which deals with nonadiabatic electronic transitions, considering the two-state approximation. I think that the author make ...
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1answer
93 views

How do I know whether the description of an electron state is complete?

Let's consider an electron as part of a larger system as an atom consisting not only of a nucleus but also of several other electrons. I guess, one can characterize the atom quantum-mechanically in a ...
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1answer
86 views

Is a bound state a stationary state?

In Shankar's discussion on the 1D infinite square well in Principles of Quantum Mechanics (2nd edition), he made the following statement: Now $\langle P \rangle = 0$ in any bound state for the ...
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1answer
58 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 ...
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2answers
46 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 ...
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1answer
66 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 ...
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1answer
153 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 ...
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2answers
78 views

Relation between giving the form of an operator in a given representation, and bra ket notation [closed]

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 $\langle r|\psi \rangle = \psi(r)$, ...
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4answers
130 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 ...
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0answers
34 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 $$A_{nm}(t)=A_{nm}e^{\frac{i}{\hbar}\omega(nm)t}$$...
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0answers
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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?...
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3answers
211 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 ...
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1answer
87 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 ...
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1answer
51 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)*\...
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1answer
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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|...
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2answers
126 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
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1answer
106 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 $...
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2answers
137 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 ...
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2answers
112 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
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1answer
52 views

Entanglement in quantum physics [duplicate]

Mathematically what is the difference between pure separable state and entangled state ? Can anyone explain with equations?