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Questions tagged [quantum-states]

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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
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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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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
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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
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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
100 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
40 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
116 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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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
85 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 ...
2
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1answer
69 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
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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
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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
64 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
147 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
63 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 $\langle r|\psi \rangle = \psi(r)$, ...
2
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4answers
115 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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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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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
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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
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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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0answers
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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^{...
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1answer
46 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|...
3
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2answers
107 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
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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
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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
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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 ...
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1answer
48 views

Entanglement in quantum physics [duplicate]

Mathematically what is the difference between pure separable state and entangled state ? Can anyone explain with equations?
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36 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 ...
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0answers
50 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 ...
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2answers
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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 ...
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0answers
54 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)...
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1answer
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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 ...
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4answers
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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 ...
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1answer
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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, ...
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1answer
64 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^...
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1answer
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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 ...
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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 $|\phi\rangle \otimes |\psi\rangle$). (...
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0answers
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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 ...
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1answer
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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 ...
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1answer
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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 ...
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1answer
61 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 ...
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2answers
279 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
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1answer
57 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=(\...
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1answer
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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 ...
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1answer
164 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{...