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 ...

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What information is contained in the quantum spectral density?

Consider a harmonic oscillator system with Hamiltonian $$\hat{H} = \frac{1}{2} a \hat{u}^2 + \frac{1}{2} b \hat{v}^2 \qquad [\hat{u}, \hat{v}]=i \gamma $$ where $a$, $b$, and $\gamma$ are all real. ...
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7 views

Spontaneous breaking order and the Peierls order

From this this Ref, several types of orderings are considered. Question: What are the Hamiltonians which support the Peierls order? Do they necessarily break translational symmetry or break the ...
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10 views

Nuclear spin relaxation, quasi-particle energy and spin spectral density

Below is a measurement of the longitudinal nuclear spin relaxation ($1/T_1$). Ref: Fig 4 of page 24 Competing ground states in low dimensions. My question concerns the statement in this Ref that: ...
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1answer
25 views

Boundary Conditions in a Step Potential

I'm trying to solve problem 2.35 in Griffith's Introduction to Quantum Mechanics (2nd edition), but it left me rather confused, so I hope you can help me to understand this a little bit better. The ...
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25 views

Hydrogen 2p3/2 -> 1s1/2 transition polarisation and angular distribution

Could you please help me. I have to calculate the intensity angular and polarisation distribution in hydrogen electric dipole transition $\text{2p}_{3/2}\rightarrow \text{1s}_{1/2}$. To do this I ...
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1answer
37 views

How do we normalize a delta function position space wave function? [duplicate]

I have a position space wavefunction $$\psi(x) = \delta(x-a) + \delta(x+a).$$ Now the question states to compute the following: The Fourier transform of $\psi(x)$. (Which invariably is the momentum ...
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25 views

Is FTL information transfer possible in an experiment involving entangled particles and an “available” black hole?

We consider the classical entanglement experiments involving Alice and Bob, and their entangled particles. It is proved that nothing that happens at Bob's end has any immediate effect on Alice's ...
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41 views

In interpretations of QM where the wave function is real, does it physically expand to infinity?

I know mathematically it does, but in interpretations like MWI and de broglie, does the wave function physically expand to infinity. Or what about the objective collapse interpretations (GRW, ...
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2answers
45 views

Why don't we have particles whose wavefunctions are symmetric wrt one exchange operator and anti-symmetric wrt other exchange operator?

Consider a system with $n$ identical particles. Let the wavefunction of the system be $\psi(r_1,\ldots, r_2)$. Let $P_{a,b}$ represent the exchange operator which exchanges particle $a$ with particle ...
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15 views

Electron wave function question?

In interpretations of Quantum Mechanics that are Psi Ontic, in which the wave function is REAL ( Objective collapse theories, MWI, ect), does the wave function still physically spread to infinity? I ...
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Calculation of the Lowest Energy of the trial wavefunction [on hold]

After a calculation of the lowest energy using two variational parameters a and b it is found that: E(a,b) = (3a+b)^2 - ab What is the optimal (minimum) value of E If I expand the bracket and ...
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1answer
49 views

Configuration Space And Hilbert Space For A Physicist Without Knowledge Of Analysis

I have passed calculus course, have basic knowledge of complex numbers and passed introductory linear algebra course. I am trying to study Griffith Quantum Mechanics book, but I am also checking some ...
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2answers
37 views

Slater's determinant for Bosons/Symmetric Particles?

For Slater's determinant it is obvious how this describes two or multiple fermions/anti-symmetric particles. By definition the determinant introduces a negative sign in front of the second product. ...
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19 views

Expectation value calculation using Hermite polynomials [on hold]

I am facing this problem of not being able to correctly determine $x^2$ expectation value using the eigenfunction for harmonic oscillator involving Hermite polynomials as derived in the analytic ...
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1answer
46 views

Why $2j+1$ number of states?

In this statement from Modern Quantum Mechanics by J.J. Sakurai: If $j$ is an integer, all $m$ values are integers; if $j$ is a half-integer, all $m$ values are half-integers. The allowed ...
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1answer
40 views

What is the implication that the Schrodinger equation be solved by both real and imaginary part of the wave function? [on hold]

Suppose $\psi = \psi_{real} + i \psi_{imag}$ be the wave function, then both $\psi_{real}$ and $\psi_{imag}$ can be used to solve the Schrodinger's equation This can be demonstrated by plugging ...
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1answer
81 views

Connections between classical mechanics and quantum mechanics [duplicate]

I've been studying quantum mechanics and classical mechanics for a little while now, and I still don't feel as though I fully understand the motivation for some of our choices in Heisenberg mechanics. ...
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5answers
184 views

How do we know that electron wave function extends to infinity?

Why do physicists assume this? Is it a proven fact that wave function extends to infinity or just a theory? Would it make sense if they didn't extend to infinity?
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34 views

black body simulation

black body radiation is typically understood from Planck's argument of light resonance in a box, from which the density of states is computed. Now, suppose I want to simulate a black body ...
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51 views

Many-worlds interpretation

Regarding many-worlds interpretation as an alternative explanation to Copenhagen. If we take the generation or possibility of alternative universes as an explanation for the collapse of wavefunction ...
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40 views

wavefunction and contextuality

According to the French philosopher Michel Bitbol, the "deep-lying connection between the contextual character of observables, and the wave-like form of probability distributions was demonstrated ...
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35 views

What is the propagator? [on hold]

What is the propagator? According to Each path is allowed. So it is possible Particle velocity faster than the speed of light?
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3answers
72 views

Expected value of $xp$ in harmonic oscillator [on hold]

I wanna find out the expected value of the $xp$ operator for the $n$-th excited state of the harmonic oscillator, i.e. calculate the value $\langle n|xp|n \rangle$. I express the position and momentum ...
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31 views

Is time depending on the observer in string theory?

I heard that in the theory of relativity the time of an action is depending on the observer. But in string theory, is the time also depending on the observer? Are strings acting according to the ...
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2answers
37 views

Magnetic quantum numbers - axes correspondence

We know that the magnetic quantum number describes the space orientation of an orbital within an atom. For the $p$-orbital, the magnetic quantum numbers can be -1,0,1 (one for every axis). We have ...
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2answers
118 views

Why are the quantum numbers $n$ and $\ell$ denoted with those letters?

We have 4 quantum numbers: principal, azimuthal, magnetic and spin (denoted $n$, $\ell$, $m$ and $s$ respectively). I assume $m$ and $s$ are simply the initials of 'magnetic' and 'spin'. Is there any ...
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1answer
69 views

The fine structure constant - can it genuinely be a random variable?

The question Does it make sense, and are there physical reasons to think about the fine structure constant as a (very concentrated) probability distribution rather than a single real number? ...
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1answer
98 views

QEC and QED with unlimited computational power - how precise they are going to be?

My question is about quantum algorithms for QED (quantum electrodynamics) computations related to the fine structure constants. Such computations (as explained to me) amounts to computing Taylor-like ...
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19 views

Lindblad equation derivation

I'm reading A simple derivation of the Lindblad equation. It introduces a Hamiltonian for a system consisting of a principal system $S$, a heat bath $B$ and an interaction term: ...
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39 views

Path integral method for harmonic oscillator [on hold]

Use the path integral method to calculate the transition $\langle x(f),t(f) \rvert x(i),t(i) \rangle$ for a harmonic oscillator.
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17 views

Landau levels. Gauge symmetry [on hold]

If we try to find wave function for different vector potential, we will get wave functions, that do not have the same probability at any point( $|\psi_{E,p_y,p_z}|^2 \neq |\psi_{E,p_x,p_z}|^2)$ For ...
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0answers
61 views

$e^{\mp i \pi \hbar S_z } S_{ \pm} e^{ \pm i \pi \hbar S_z} = -S_{\pm}.$ [on hold]

I am supposed to show that $$e^{\mp i \pi \hbar S_z } S_{ \pm} e^{ \pm i \pi \hbar S_z} = -S_{\pm}.$$ I tried things like the Hadamard equation, but did not really get close to this equation. Does ...
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32 views

Resource cost and noise effects in quantum teleportation of multible (entangled) qbits

Suppose you have n qubits that are in an unknown state (may be entangled, etc). Can you teleport this state by teleporting each qubit individually (using a Bell state and a classical channel)? If ...
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1answer
27 views

How to determine whether an eigenstate of total spin is symmetric or antisymmetric?

Here we have two identical paticles with spin $I$, integer or half-integer, and there are $(2I+1)^2$ states. Each one of them can be uniquely determined by total spin and its orientation, we can use ...
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2answers
83 views

Proving (instead of discovering) the laws of quantum mechanics

A single toss of a fair coin cannot be predicted. But if we observe a large number of tosses, we can prove mathematically the law that roughly half of them will show up heads. The movements of ...
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2answers
69 views

What's the true reason behind thermal expansion?

Thermal expansion is a normal concept everyday. There are 2 explanations: 1, thermal expansion result in stress, then result in deformation 2, thermal expansion result in deformation, then result in ...
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3answers
108 views

Do electrons pop into and out of existence around the nucleus of an atom?

What surrounds the nucleus is the probability wave. But are the electrons constantly popping in and out of existence around the nucleus in the cloud?
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1answer
48 views

What is the energy of a Gaussian wave packet?

Suppose we have a potential barrier situation, that is $V(x)$ is zero everywhere except on the interval $[-a,a]$, where it is equal to some $V_0 > 0$. Introduce some Gaussian shaped wave packet to ...
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1answer
47 views

What does vector space and bra/ket space mean? [on hold]

I wonder What are the similarities and dissimilarities between a vector space and bra/ket space?
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31 views

Determining Parity of Decaying Quantum System

Show that a particle of spin $1$ cannot decay into two identical particles of spin $0$. The $\rho$-meson has spin $1$ and can decay into two spinless (spin-$0$) $\pi$-mesons, or pions, with ...
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6answers
521 views

On the foundations of quantum physics

Quantum physics has to be validated by experiments. But experiments are to be interpreted in the context of quantum physics. Isn'it like a snake biting its own tail? For example, using a scanning ...
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2answers
275 views

Entanglement and simultaneity

According to the special theory of relativity, distant simultaneity depends on the observer's reference frame. And, according to the quantum theory, in the case of two entangled particles, a measure ...
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0answers
84 views

A problem with the Gamow state

Consider a form of potential $U(r)$ as follows $$ U(r)=\begin{cases}0 & 0<r\leq a \\ U_0 & a<r\leq b \\ 0 &r>b\end{cases} $$ In this problem $r$ is the distance from the origin, ...
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1answer
19 views

In what order will the magnetic quantum number be filled

For example, the electron configuration for Cu(II) ion is [Ar]3d9. So only the 3d shell matters to the total orbital angular momentum of the ion. For 3d shell there are 5 possible values of $m_l : ...
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1answer
45 views

Does a static electric field act continuously?

Electromagnetic radiation is emitted and absorbed in discrete units, photons. One photon's energy is described by the well known $E = hf$ formula. Now, if you a have static electric field that ...
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84 views

Are there any proposed alternatives to quantum mechanics as there are alternatives to general relativity?

There are a lot of alternatives to general relativity and one of the motivations is attempting to formulate a working theory of quantum gravity. In some limit they reduce to general relativity. But ...
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30 views

Show that a barrier which is forbidden for a classical particle can have a finite probability for a quantum particle [closed]

Show that a barrier which is forbidden for a classical particle can have a finite probability for a quantum particle.
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1answer
110 views

Should the differential of a wavefunction have a time partial derivative?

In chapter 1 of Griffths' QM text, he shows that $\frac{\mathrm{d}}{\mathrm{d}t}\int_{-\infty}^{\infty}|\Psi|^2\,\mathrm{d}x=0$ by noting $$\begin{align} ...
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1answer
35 views

How does observer affects the wave-particle nature ? (and related questions: part 2)

Following comments I split my question in to two parts which are independent. The questions are about double slit experiment with an observer(s). Suppose electrons are being used in the experiment ...
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1answer
74 views

Degrees of freedom in Quantum Mechanics

If we look at a particle in classical mechanics, the degrees of freedom increase as its size decreases like the degrees of freedom of an atom is more than that of molecule, and subsequently, the ...