Questions tagged [quantum-mechanics]

Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.

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Umbrella name for both creation and annihilation operators [closed]

I'm getting really sick of writing creation and annihilation operators. It seems long and clunky to me. Is there a shorter name for referring to these operators? I'm tempted to just write the ...
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What is the definitive evidence we have that quantum theory's probabilistic nature is physical and not epistemic?

For example does superposition or wavefunction really occur in the physical quantum world or is it only a property of the quantum theory's framework and formalism to help us to make accurate ...
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Is Rubidium used in Photoelectric cell?

The question is pretty straightforward . I know that Potassium and Caesium are (famously) used for the purpose . Further Rubidium lies midway between Potassium and Caesium in s-block and hence a lot ...
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Bohr's first criticism in his theory [closed]

On what theory of classical electrodynamics was the first criticism of Bohr's model of the atom based on?
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Why must systems of identical particles be either totally antisymmetric or totally symmetric? Why can there not exist a mixture?

I am reading chapter 6 of Sakurai's Modern Quantum Mechanics and have come across the 'symmetrization postulate', which tells me that for any given system of identical particles, all states must ...
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Integral of eigenkets (QM)

I'm reading Dirac's book about QM. I reached the point (in my edition on page 37) where he tells it is possible, given the eigenkets of an observable, express any other ket in function of them (as he ...
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Average of Two successive momenta $m\frac{x_{k+1}-x_k}{\epsilon}m\frac{x_k-x_{k-1}}{\epsilon}$ using rules of path integral

A Problem from Feynman's Path Integral Book Let $x_i$ be coordinates at different time instances, prove that $$ \langle\chi|m\frac{x_{k+1}-x_k}{\epsilon}m\frac{x_k-x_{k-1}}{\epsilon}|\psi\rangle=\int\...
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Least action principle and its quantum mechanical view [duplicate]

In Feynman's lecture (I am forgetting the volume number) while explaining the least action principle he mentions that the system actually follows all possible configuration paths. $\exp(iS/\hbar)$ ...
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How to show the hermiticity of an operator? [closed]

Rq(x)=Aq(x+a). R and A are operators, q(x) a wavefunction. A and a are real and positive. Find the relationship between A and and a such that R is hermitian.
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Is there a Noether's theorem in quantum mechanics in the path integral formalism? [duplicate]

Here is a discussion that talks about Noether's theorem in quantum mechanics in its Hamiltonian formulation. It tells how symmetries give rise to conserved quantities. However, we know that there also ...
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Can the Auger effect cause a second electron to be just excited instead of ionised and emitted from the atom?

From what I understand, the Auger effect is usually defined as when an electron deexcited but instead of releasing its change in binding energy as a photon, it transfers it as kinetic energy to ...
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Change of Mutual Information in Isolated Quantum Systems

I was reading some publications regarding correlation and mutual information for composite quantum systems. I noticed that most papers give the expression for the mutual information to be: $$\Delta I(...
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Is the motion of proton in EM described by the Schroedinger equation?

Does the usual Schroedinger equation describing the non-relativistic motion of electron in electromagnetic field also describes non-relativistic motion of proton? (Of course the values of charge and ...
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Non-locality of pre-Klein-Gordon equation

In Relativistic Quantum Mechanics, Bjorken and Drell state that expanding the square root in the equation $$-\hbar^2\frac{\partial^2\psi}{\partial t^2}=\sqrt{-\hbar^2c^2\boldsymbol{\nabla}^2+m^2c^4}\...
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How does the electron understand that it being observed in the double slit experiment?

I was reading about the double slit experiment that proved the wave and particle nature of electron. I read that electrons give a diffraction pattern when they are not observed (wave nature) and ...
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Simultaneous observables

Hi I understand that when two observables are simultaneous we can measure them both at the same time without affecting each other however is there a condition that the commutator between the two ...
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Young's Modulus and Shear Modulus relationship [closed]

Suppose a 3D simple cubic crystal in which nearest-neighbor atoms are bound by springs with equilibrium length = lattice constant $a$ and spring constant $C$. How can I find Young's modulus $C_{11}$, ...
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Yukawa interaction in QM (0+1D field theory)

This is a question about considering a simple ordinary quantum mechanics system from a quantum field theory perspective. Out of necessity the setup describing the problem is fairly long, but the ...
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(Paradox) can orbital angular momentum possible values be continuous?

If my understanding of Quantum mechanics is valid then a spinless particle can be in a physical state associated with a combination of sharp (having a almost a delta function profile of a normalizable ...
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Partial Trace of correlated states

If given a state of the form $\rho_{AB} = \rho_A \otimes \rho_B$, I know that the partial trace with respect to one of the two subsystems will return me the reduced density matrix of the other: $$\...
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Doubt about the Gaussian state

I am reading an article that makes an application using the Gaussian state. The author of the article writes the Gaussian state as follows: $$\psi(q) = [2\pi(\Delta q)^2]^{-\frac{1}{4}}e^{-\frac{q^2}{...
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Problems deriving the Quantum Hamilton-Jacobi equation

This is my first question at Physics SE so please be kind. I am well versed in the etiquette over at Math SE, but not so much here. Anyway, I thought this question was better suited to this site ...
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Matrix elements of operators in position representation

In a lecture note, it is written $$ T_{ij} = \langle \phi_i| \hat{T} | \phi_j \rangle = \int d^3 \vec{r} \phi_i^*(\vec{r}) T(\vec{r}) \phi_j(\vec{r}) $$ How to obtain the second integral form from ...
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Expectation Value of an Operator in the Projector Augmented Wave Method

I'm starting on DFT and came across this technique called PAW Wave Method for multi atoms system wave function. It is a widely employed method in DFT calculations. From the attached picture, I'm ...
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Do “functions” always refer to “wavefunctions” in quantum mechanics?

For example, what do we mean when we say that “Operator acts on the function that follows it”? What are the examples of “functions” that operators act on (in quantum mechanics)?
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Limits of Physically Realizable Evolutions

Quantum Mechanics tells us that every unitary evolution operators is physically realizable (if a universal quantum computer exists...). I am curious to understand what that ultimately means. What do ...
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Memory effects in open quantum systems: Markovian approximation question

Setting: Quantum system $S$ composed of a subsystem of interest $A$ and a subsystem acting as the environment $B$ such that $S=A\cup B$. System $S$ is described by density matrix $\rho$ whereas ...
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Troubles in Dirac's “Principles of quantum mechanics”

I'm reading the Dirac's book about QM and I am finding troubles understanding a proof of a theorem (in my edition at page 32), which says that "there are so many eigenkets of $\xi$ that any ket ...
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Qubits vs Gravitational Waves

I've read that Qubits must be shielded from all external noise, since the slightest interference will destroy the superposition, resulting in calculation errors. Question Are Gravitational Waves a ...
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How $[x,p]=i \hbar$ implies that $x$ and $p$ do not have simultaneous eigenstates?

I am reading Quantum Comuputing Explained by David McMohan. Here is a portion which I am not able to understand. Let $x$ be the position and $p$ be the momentum of the particle, then we know that $$[...
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Theorem in Dirac's “Principles of quantum mechanics”

I'm pretty new to quantum mechanics and after reading the Susskind's book I dived into the Dirac's one. I've managed to understand until this theorem has been enunciated (in my edition at page 32): &...
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Uncertainty principle and multiple-slit diffraction

Most of the quantum mechanics textbooks mention the single-slit diffraction phenomenon and explain it with uncertainty principle to obtain the $b\sin(\theta)=n\lambda$ law. But how does one explain ...
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Is the effective Hamiltonian obtained via Feshbach-Fano partitioning closed?

I am not familiar with Feshbach-Fano partitioning so this question may be trivial. The full Hamiltonian of an open quantum system consists of system+enviroment+interaction. This can be cast into an ...
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Infinite linear potential well?

I am currently learning and solving Schrodinger's time independent equation for particles under various 1D-potentials. Would it be possible to have a mix of a linear potential (of the form $U(x)=Fx$ ...
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Momentum in a quantum particle in a box

The momentum operator in one dimensional quantum mechanics is: $$\hat p_x=\frac{\hbar}{i}\frac{d}{dx} $$ and we can imagine creating an eigenvalue-eigenfunction system $$\hat p_x\psi = p_x\psi.$$ As a ...
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Could anyone help me understand this article on the Many Worlds Interpretation? [closed]

https://arxiv.org/pdf/2001.03771.pdf I am struggling to understand this paper because the depth in which the subject is discussed is much greater than my own. The topic is highly interesting to me, so ...
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Propagator for a free particle with a position dependent mass?

I understand that the propagator for a free non-relativistic particle with a fixed mass has the closed-form $$ \sqrt{\frac{m}{2 \pi i \hbar t}} e^{\frac{i}{\hbar} \frac{m}{2 t}(x_i - x_f)^2} .$$ I was ...
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Why is the first derivative of the time-dependent Schrödinger equation continuous? Where does it come from?

I was taught in first year physics that the first derivative of the time-dependent Schrödinger equation had to be continuous. However I was never taught (or at least I don't remember) the reason why. \...
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Time ordering on Kelydsh countour

I want to compute a time-ordering product but I have a question concerning this time ordering product. First, we consider A,E,I,L,N,O and V some second quantized operators without specifing what ...
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Is there interferences between 2 electron wavefunctions?

The 2 slits experiment done with 1 electron shows interference from the "splitted" wavefunctions. My question is, if we sent 2 electrons simultaneously in the 2 slits and each one can go in ...
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When is the phase shift small and linear in $k$ for low energy $s$-wave scattering?

I was wondering when should we expect the phase shift to be small and linear in $k$ for low energy $s$-wave scattering, so that the scattering length can defined as $-\delta/k$, since the general form ...
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Exponential of a ladder operator justification

Considering the ladder operators of quantum mechanics, specifically the creation operator,can we take its exponential? I was looking at this post: Annihilation operator in the exponent? and in the ...
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What is the physical justification for the boundary conditions of the Schrödinger equation for an infinite potential well?

All the literature says that the physically meaningful solutions to the Schrödinger equation in an infinite potential well must fulfill the boundary condition that the wave function is $0$ at the ...
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About different eigenstates corresponding to hamiltonian orthogonality [closed]

Show that the eigenstates corresponding to different eigenvalues of a Hermitian operator are mutually orthogonal
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Balmer Continuum

I'm trying to simulate the Balmer series emission lines and am trying to compute the wavelengths. The Rydberg formula does this fine, up until the point where you're trying to model the spectrum at ...
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Why do we need large time assumption for energy conservation in electron transitions?

For electron absorption calculations (with an electric field perturbation $\Delta H = eE_0x cos(\omega t)$) we end up with an integral like: $$c_2(t) \propto \int \rho(\omega) \left( \frac{\sin(\frac{...
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Link between rotating wave approximation and stimulated emission and absorption?

In my lecture notes deriving the probability density of a two energy level atom we arive at the following equation: $$c_f(t) = \frac{1}{2} \Omega \left[\frac{1-e^{i(\omega + \omega_0)t}}{(\omega + \...
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How to motivate the Dirac equation? [closed]

I have been told that you can find the Dirac equation as follows. Start with the nonrelativistic Schrödinger equation $$i \frac{\partial \psi}{\partial t} = -\frac{1}{2m} \nabla^2 \psi + V\psi$$ (or ...
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Is spacetime entangled with a free particle?

Consider a single free particle. If a spacetime metric satisfies the superposition principle, then the full state of the particle and the spacetime should be $$\sum w_{x,y,z,t}|x,y,z,t\rangle|g_{x,y,z,...
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Is the complex conjugate of the amplitude of an electron wavefunction equivalent to the amplitude of the corresponding hole?

Is the complex conjugate of the amplitude of an electron wavefunction equivalent to the amplitude of the corresponding hole? Say I consider a wavefunction of an electron that has the amplitude A. If I ...

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