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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How to find the hermitian adjoint and inverse of an operator?

Suppose I have a translation operator defined as: $$ \hat{T_a}\Psi(x)=\Psi(x+a) \, . $$ Now, how do I find the hermitian adjoint operator as well as its inverse?
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142 views

Why does the photon strike at one or another place on the tape?

I am more than happy in accepting the wave nature of light and the fact that each of photons has probabilistic distribution "coded" within itself. But what is about the particle's part and the ...
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22 views

According to the Copenhagen Interpretation what does superposition mean? [duplicate]

I am not interested in Many Worlds Interpretation because I think it’s mental and after some personal research I found out that it wasn’t (despite some claims otherwise) popular among physicists at ...
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Can any linear but non-unitary “time-evolution operator” be normalized to a unitary one?

A comment to this answer to another question states I would imagine that for any linear non-unitary time-evolution operator, I can find a unitary one that will yield the same expectation values for ...
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Ladder operator for quantum spherical pendulum [on hold]

I am aware of this question on solving the time-independent quantum spherical pendulum problem (Quantum Spherical Pendulum), but I cannot think of ladder operators that will work, and I don't know how ...
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Rotation operator as discussed in S. Weinberg

Following the discussion on rotation operators in Sakurai made clear sense, however, due to coursework, I need to also understand the discussion provided in Quantum Mechanics by S. Weinberg. In ...
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Spintronics: How can we inject a spin current into/onto a sample without physically touching it, ie: modulation with a field?

So background, I'm imagining a black box scenario where we have some spintronic system. It might be a topological quantum computer that uses spin currents running across it's memory to connect ...
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Interpretation of annihilation and creation operators

If we write some quantum field in a form using creation and annihilation operators we are, in a way, doing a Fourier series with annihilation and creation operators being coefficients. So, if they are ...
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Planck's velocity distribution and energy of different modes of motion

The Planck's distribution describes the frequency spectrum of a classic dipole oscillator. Question: How can one be sure that the emitted black-body radiation only has vibrational energy since the ...
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Calculating a matrix element, $\langle x|p\rangle$? [duplicate]

I've often just assumed $$\langle x|p\rangle = \frac{1}{(2\pi\hbar)^{1/2}}e^{ipx/\hbar}$$ Is there a formal way to prove this? My guess is that, since $\langle x|x'\rangle = \delta(x'-x)$, and a ...
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57 views

Is this a possible interpretation of quantum tunneling?

Suppose we have a particle in a finite potential well where the potential is $V_0$ and the ensemble average momentum is $\langle p\rangle$, so that the average kinetic energy $$\langle T\rangle =\frac{...
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39 views

Uncertainty about the ensemble average?

Does an uncertainty in momentum of $\Delta p$ mean that the actual momentum is in the range $\langle p \rangle - \Delta p\space <p< \langle p\rangle+\Delta p\space$ ? Or does it mean that the ...
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Differentiability of wave function at boundary in infinite square well

I was told in class that a wave function should have the following properties: Finite and single-valued Continuous Differentiable Square integrable But if we consider the wave function in an ...
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de Broglie equation has momentum=$mv$ not $mc$. why? [on hold]

de Broglie equation that is $$\lambda=\frac{h}{mv}$$ This equation is derived from $E=mc^2$, so why is momentum taken as $mv$ and not $mc$? Because $E=mc^2$, not mv^2
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How can increasing the speed and/or mass of a particle reduce, not increase, it's frequency?

In a Physics World article called 'Neutrons on a Lab Bench', from 30 January 2013, it says, '...Yin and Albright calculated that a very intense laser beam should be able to boost the speed of ...
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Can you argue without explicitly calculate the eigenenergies that one Hamiltonian is gapped and another is not?

Consider a pair of one dimensional four band model $H_1$ and $H_2$, which read as: $$ H_1 = \begin{pmatrix}k\sigma_x-E_0&0\\0&k\sigma_x+E_0\end{pmatrix} + \alpha \begin{pmatrix}0&\sigma_x\...
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Does an Operator that neither commutes with $\hat{X}$ or $\hat{P}$, nor can be expressed as a “function” of $\hat{X}$ and $\hat{P}$ make sense?

When you come from classical hamiltonian mechanics (which is based on the phase space), observables are introduced as functions $f$ on the phase space $(q, p)$. There can't be a classical observable ...
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Question on modified particle in a box [on hold]

If say, I have a particle bound in an infinite well where the floor is very slightly sloping. How would I sketch a possible wave function when the energy is E1(no nodes)? How do we do this ...
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90 views

Bra-ket notation in a 3 dimensional system

Recently we started to learn quantum mechanics in a three-dimensional system. However, I am very confused from the beginning. Firstly, professor told us that for a position vector $\pmb{x}={}^t(x,y,z)$...
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54 views

Confusion as to whether classical or quantum statistics be used [closed]

Suppose a gas is kept at a temperature of $7000 \text{ K}$ and has a particle density of $2.7 \times 10^{34} \text m^{-3}$. Do we need to treat it quantum mechanically or will classical treatment be ...
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Does a non-stationary state for a single particle with a nondegenerate spectrum necessarily have fluctuations in probability density?

Suppose we have a single particle in 1D, with wavefunction $\psi(x,t)$, obeying the Schrödinger equation in position space: $$i\hbar\frac{d\psi(x,t)}{dt}=\left(-\frac{\hbar^2}{2m}\frac{\partial^2}{\...
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Does uncertainty principle imply that the past history of universe is also undetermined?

I read the page here: Is the Uncertainty Principle valid for information about the past?, but I am still somewhat confused. If you measure the momentum/position (with uncertainty) of a particle, what ...
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115 views

Could quantum randomness be transformed into classical, macroscale randomness?

If measurements of quantum phenomena can show results that are truly random wouldn't it be possible to establish a macroscale-dependence on such a non-statistical result and thereby introduce ...
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Can a random product state be expressed as a MPS (Matrix product state)?

$ |\psi\rangle = \prod_{i=1}^{N}|s_{i}\rangle $ where, $|s_{i}\rangle = \cos\left (\frac{\theta_{i}}{2}\right )|\uparrow_{i}\rangle + \exp{(i\phi_{i})}\sin\left (\frac{\theta_{i}}{2}\right )|\...
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Ways to calculate the mean value of Displacement operator for the coherent state? [closed]

I would be thankful any help about calculating the mean value of displacement operator for coherent state ? in exponential expansion of displacement operator, there would be terms which appear as we ...
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53 views

Why emission of an electron does not depend on light's intensity?

There's something that confuses me about the photoelectric effect. In an article I read, it's stated that the emission of an electron does not depend on the light's intensity. I'm not sure on which ...
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52 views

Is it possible to construct a state for harmonic oscillator given the mean energy?

The harmonic oscillator is defined by the mean value energy $\langle E\rangle=\frac{2}{3} \hbar\omega$. Can we have a wavefunction which describes such a state? Any help is appreciated. Is it ...
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What is the difference between feshbach resonance and shape resonance?

What is the difference between feshbach resonance and shape resonance in general and also in the case of ion-atom collisions
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Is there an accepted way to plot a wave function and the potential?

When using the time-independent Schrodinger equation and finding a wave function $\psi(x)$ for a given potential $V(x)$ is there a consistent way to plot these two objects on the same image that takes ...
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Unphysical initial state for some quantum system

Let's say that I have some quantum system defined by Hamiltonian $\hat{H}$. The energy eigenstates of this Hamiltonian form a complete basis for the Hilbert space of all possible states corresponding ...
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Is the group velocity times the phase velocity always the velocity of light squared?

Can there be cases where it is different from $c$ squared? If so in what situations would it differ?
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67 views

Harmonic oscillator with potential shifted by a constant

I've been thinking a lot about changes to the harmonic oscillator potential, and I was looking into the problem where $$V(x) = \frac{1}{2}m\omega ^2 x^2 + C$$ where $C$ is some positive real ...
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21 views

Momentum from Position Probability Density of a Quantum System

Suppose there are four possible eigenvalues of position {1,2,3,4}. We have a single particle present in this system. Now suppose we have a process by which we can measure the eigenvalue of this system....
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Identity reversing event

I'm a master student in mathematics currently taking Quantum Mechanics and since the lecture notes provided by the lecturer aren't cutting it I'm reading "Quantum Mechanics and Path Integrals" by R. ...
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Why does transition from one electron shell to another shell always produce massless photon?

When electrons transition from a higher energy state to a lower energy state (energy difference $E$), they produce massless photon with frequency $\nu$ where $ \Delta E= h \nu$ (h is Planck ...
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If $E$ and $P$ don't commute, why could we have an $E$-$K$ diagram?

If $E$ (energy) and $P$ (momentum) only commute in constant potential, how could we have an $E$-$K$ diagram in a solid material? $[E,p] \neq 0$. Then we cannot prepare electrons whose $E$ and $P$ are ...
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What is a quantum system?

I heard that a wavefunction applies to a quantum system. But what is a quantum system? I am new to quantum mechanics, sorry for asking a basic question.
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Eigenvalues and Eigenfunctions for a function of an operator?

For my quantum homework, I was asked to prove if $f(x)$ is an eigenvector of $F(\hat{A})$ where $F$ is given as an "arbitrary differential function" and $f(x)$ is a known eigenfunction of $\hat{A}$ ...
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Connection between Group of Schrodinger equation and energy level degeneracy [duplicate]

I am recently study group theory and its application in quantum mechanics, but got stuck at a very important point that how group theory can be applied to analyze energy level degeneracy. In many ...
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311 views

Writing operators in the position basis

To calculate an expecation value in quantum mechanics of some operator $\hat A$ you can generally write it in Dirac notation $$\langle \hat A\rangle=\langle\psi|\hat A|\psi\rangle.$$ In the position ...
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Derivation of quantum virial theorem

The quantum virial thoerem is derived by arguing that the left-hand-side of the following expression is zero for stationary/bound states: $$ \frac{d}{dt}\langle{\bf{r} \cdot \bf{p}}\rangle = \bigg\...
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Central Potential + Coupled Angular Momenta

I am considering a two-state system with a Hamiltonian of the form $$ H = \frac{p_1^2}{2m_1} + \frac{p_2^2}{2m_2} + V_a(|r|) + \bigg(\frac{1}{4}-\frac{S_1\cdot S_2}{\hbar^2}\bigg)V_b(|r|), $$ where ...
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56 views

How important is quantum mechanics to solid state electronics? [closed]

How important is it to know quantum mechanics if one wants a career in solid state electronic devices? I want to do a PhD in semiconductor physics, but I don't know much quantum mechanics. What do ...
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Energy eigenstates using matrices

I just learned that derivatives can be represented as matrices. So, I was wondering if I could write the $\frac{d^2}{dx^2}$ and $V(x)$ as a matrix, maybe I could treat the eigenvalue problem, $${\bf ...
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Shared link between non-relativistic QM and Special Relativity: Proper time? [on hold]

So in the path integral formulation of QM, each path gets weighted by a phase factor of $e^{iS/ \hbar}$, where S indicates the classical action of the path. For a small displacement in space and time (...
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118 views

Successive amplitudes in quantum mechanics

In quantum mechanics we define amplitudes for events, like propagation from one point to some other point. Lets say that from a source to detector we have some amplitude (D/S). But, lets now say that ...
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38 views

Writing total angular momentum eigenstates in terms of spin and orbital angular momentum eigenstates

I want to understand how we can derive the simultaneous eigenfunctions of the total angular momentum operator and the z component of the total angular momentum operator in terms of the orbital angular ...
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What (in silico information) defines the transfer function of a Quantum Amplifier, in the form of a molecule?

Let’s say a team of scientists have published the structure of a molecule they claim acts as a quantum amplifier. Photons travel along a quantum channel carrying qubits in their polarization. The ...
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39 views

Is there a second/many order form of the infinitessimal unitary operator in quantum mechanics?

Is there a second/many order form of the infinitessimal unitary operator in quantum mechanics? We know that a unitarily transformed system must be invariant, i.e. $\langle\psi|\psi\rangle = (\langle\...
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46 views

Eigenstructure of the Dicke Model

I am beginning a study of the Dicke model and found a very interesting publication: "The Dicke model in quantum optics: Dicke model revisited" by Barry M Garraway in Phil. Trans. R. Soc. A (2011). I ...