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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Probability density function as number of particles per unit volume?

In this book Quantum Mechanics by P.J.E. Peebles pg 365 it hints at the idea of the wave function been the probability of finding $n$ particles per unit volume. I have looked in other books and on ...
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1answer
22 views

Can the uncertainty principle be redefined for different standard deviations?

$$\sigma_x \cdot \sigma_p \ge {{\hbar} \over {2}}$$ Where the $\sigma$ is the standard deviation. What happens to the inequality if you use a different definition of $\sigma$. For instance what ...
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1answer
28 views

Why can the probability function for a particle in an infinite square well be larger than 1?

For a particle in a one dimensional infinite potential well of width $L$ the probability function is: $$P_n(x)=\left(\frac{2}{L}\right)\sin^2\left(\frac{n\pi x}{L}\right)$$ for $0\leq x\leq L$. The ...
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14 views

What makes electrons behave like particles or waves at different times? [duplicate]

I am quite puzzled about the theory that electrons or light often behave as particles and sometimes as waves. So, I wanted to know more about this phenomena and what happens when and why.
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1answer
23 views

Is harmonic oscillator continuous variable system?

In the literature I have seen that the notions "our system is continuous variable system", "Hilbert space of our system is infinite" were used as if they were equivalent. For example for harmonic ...
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9 views

Spin-orbit coupling of low band gap vs large band gap semiconductors

Why do low band gap material III-V semiconductors, like InAs, show a spin orbit coupling effect higher than large band gap semiconductors? Please give me some references if possible.
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35 views

Why is it easier to calculate $\langle \chi|j\rangle\langle j|A| i\rangle\langle i| \phi\rangle$ than $\langle \chi|A|\phi\rangle$?

I was reading Feynman lectures III's Spin One; there at the machinery of quantum mechanics he discusses a situation in which he needs to find the amplitude of finding the particle at ${\chi}$ state ...
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23 views

What causes the Shubnikov-de Haas Oscillations?

If I have a 2DEG with a voltage in the $x$-direction and a $B$-Field in the $z$-direction (so I also get a hall-voltage in the $y$-direction (classicaly)). But if I do this stuff at low temperatures I ...
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1answer
21 views

Delayed choice measurement subsequent analysis

This is a variant associated with the Scully and Druhl signal-idler photon delayed choice experiment, as described and discussed in Brian Greene's Fabric of the Cosmos. The commentary notes the ...
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53 views

Is there a quantum mechanical analog to classical rheonomic constraints wherein the Hamiltonian is not the total energy?

The Wikipedia article on the Hamiltonian operator in QM says that the Hamiltonian corresponds to the total energy of the system, but qualifies that statement with a "in most cases" tacked on the end. ...
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2answers
52 views

If $[A_1, H] =[A_2, H] = 0$ but $[A_1, A_2] \neq 0$, $H$ must be degenerate?

I am having a difficult time understanding this problem. Suppose $[A_1, A_2] \ne 0,$ $[A_1, H] = 0,$ $[A_2, H] = 0.$ Show that the energy eigenstates of $H$ are in general ...
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2answers
58 views

Physical Meaning of Phase Ambiguity

What is the physical significance of multiplying a quantum state $|A>$ by a phase factor $e^{i\theta}$. This does not have any effect on the normalization of the state so what is it physically? ...
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17 views

Photons absobtion during quantum jump

According to this article a quantum jump CAUSES photons absoptions. Does it mean that if there is no photon around quantum jump is impossible? https://en.wikipedia.org/wiki/Atomic_electron_transition ...
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3answers
108 views

Is Hamiltonian a differential operator in second quantization?

Normally, a free particle Hamiltonian is written $$ \hat{H} = - \frac{\hbar^2}{2m} \Delta $$ which is a differential operator because Laplacian $\Delta$ is. On the other hand, in second ...
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1answer
28 views

Resistance of a cloud of free electron gas by Kubo formula?

How much is the resistance of a cloud of free electron gas, if at all? How much is the resistance of a cloud of free electrons in a periodic potential? Did anyone calculate it using the Kubo ...
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2answers
89 views

Do atoms behave like waves? [duplicate]

I've heard someone state that the double slit experiment can also be done with atoms, not just electrons or photons of light.
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0answers
34 views

Approximate Electric Potential $V$ so that it is of the form $V(r) + V(\phi) + V(z)$

I'm trying to simulate the conductivity of a nanowire that is modeled by a cylindrical shell of infinite potential with benzene rings in the core of the wire. (This is based on a coiled-coil protein ...
2
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1answer
48 views

What is the physical significance of Compton wavelength?

Wikipedia says, The Compton wavelength represents the quantum response of mass to local geometry. What does it actually mean?
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2answers
206 views

Electron as a standing wave and its stability

1. When it was an era of classical mechanics we used to believe in the Bohr's atomic model. It interpreted electrons as particles (although I couldn't understand how come Bohr who interpreted ...
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1answer
38 views

Can we extract positrons from gamma rays?

If gamma rays undergo pair production is there a way to say, deflect and collect the positrons using magnetic fields?
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1answer
68 views

Question about Planck's constant

How did Dirac or whoever came up with it know that the momentum operator in quantum mechanics is $-i\hbar\frac{d}{dx}$? How did he know the $\hbar$ was in there? How did all these physicists know ...
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1answer
59 views

Basis states for many-particle system

I'm reading these notes about second quantization. In section 1.4 the author introduces many-particle wavefunctions. But I can't understand how basis are defined here. I know that if $\{\chi_i | i=1, ...
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3answers
99 views

Wave Function concept

What do we mean when we say wave function of electron? Does it mean wave nature of electrons? I am really confused.Without clearing this confusion i cannot proceed to molecular orbital theory.I am ...
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1answer
22 views

Semi-infinite / Asymmetric potential well

I'm asked to come up with an ansatz and solve for the coefficients of a asymmetric infinite potential well, where: $$ V = \begin{cases} \infty \text{ for } x< 0 \\ V_0 \text{ for } 0 \leq x \leq L ...
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2answers
22 views

What happens to a radioactive element or isotope's electrons when it undergoes alpha decay? [duplicate]

It seems to make sense that when an atom loses two protons, it would lose two electrons as well, but I don't actually know what happens.
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1answer
44 views

Light changes wavelength in the presence of gravity, can the quantum theory of gravity explain this?

If light changes wavelength in the presence of a gravitational field, how can this be described by the quantum theory of gravity?
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1answer
29 views

Circular polarisation destroying interference pattern for double slit

I have been trying to mathematically explain the empirical result that putting orthogonal polarisers (quarter-wave plates) behind the two slits of a double-slit setup will erase the interference ...
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46 views

Does Only Flat universe have zero energy? [on hold]

Hello I am very new to cosmology and quantum physics. I need some basic understanding (in LAYMANs term )of the following: I read that only closed universe has zero energy. But I heard Astrophysicist ...
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39 views

which of the many interpretations of Quantum Mechanics most well explained? [on hold]

I have been studying the ensemble interpretation by Leslie Ballentine which looks very well explained and has reason for every(almost every) axiom. I am seeking new your opinion.
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26 views

How does Quantum tunneling conserve energy? [duplicate]

How does Quantum tunneling conserve energy? Take a simple example. An electron in hydrogen leaves the single proton it was bound to and escapes without being excited by and interaction. It tunneled ...
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1answer
35 views

Derivation of minimum uncertainty from Squeezed Coherent State [on hold]

I'm studying a book in which I stopped by this point. I don't know how to derive the inequality from $$tr(\rho A^{*}A )?$$
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0answers
61 views

Modern Quantum Mechanics, Sakurai [on hold]

As a graduate student am I supposed to finish the entire material of "Modern Quantum Mechanics, Sakurai" ?
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0answers
98 views

Can the Born rule be derived? [duplicate]

$\renewcommand{ket}[1]{|#1\rangle}$ If we have a particle and we know the initial state $|\psi\rangle$ of everything that is relevant, and we know the full Hamiltonian $H$, then we should be able to ...
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23 views

How to write electron hole Hamiltonian into quasi-boson form?

V Chernyak, Wei Min Zhang, S Mukamel, J Chem Phys Vol. 109, 9587 (can be freely downloaded here http://mukamel.ps.uci.edu/publications/pdfs/347.pdf ) Eq.(2.2), Eq. (B1) Eq.(B4)-(B6). When I substitue ...
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1answer
88 views

What is the classical counterpart of an eigenstate?

Does this question make sense for every system or just some? If it makes sense, it is a periodic orbit?
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3answers
49 views

How does one describe a state with a density matrix after measuring position?

My question is about position measurement in non relativistic quantum mechanics. I've been taught that when you measure the value of an observable for some state of a system described by ...
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1answer
31 views

Convex combinations of states yielding a pure state

Wikipedia states that Geometrically, when the state is not expressible as a convex combination of other states, it is a pure state.[9] The family of mixed states is a convex set and a state ...
1
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1answer
228 views

Total orbital and spin angular momentum for a closed shell

I read one Phys.SE question similar to mine, in Total angular momentum in a full shell but the question was so confusing and vague. The answer, though, was helpful for me to understand a part of my ...
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1answer
36 views

How is work function for a metal in photoelectric effect just one single number?

I mean,there are so many electrons at different positions on the surface of the metal,at different depths with different energies. how is it possible that work function for all the electrons same? is ...
1
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1answer
56 views

Can a photon excite an electron via the uncertainty principle?

An electron is trapped in an infinite well potential with a width of $\Delta x$. A photon of wavelength $\lambda $ < $\Delta x$ is fired at the electron and misses or rather they don't interact. ...
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5answers
803 views

Double-slit experiment: Difference between observing photon path and interference pattern?

This is something that has confused me whenever I read about the double-slit experiment. When the double-slit experiment is performed, I understand that the resulting pattern for the sequentially ...
2
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1answer
50 views

Smoothness of the energy levels of a generic Hamiltonian

Let us take an Hamiltonian $H(\xi)$ which depends on a set of parameters $\xi$, and assume that the matrix elements $h_{ij}(\xi)$ of the Hamiltonian are smooth complex functions of the parameters ...
2
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2answers
122 views

Proof that entanglement is independent of distance

I've already read this quite often but never seen a proof—maybe it's just so clear to physicists, but I'm not really sure how to prove it. Currently I'm pretty confused so the following might be ...
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2answers
33 views

How to express a convex function of a Hermitian operator in terms of its eigenvalues and eigenvectors?

The Hermitian operator $\hat O$ can be expressed as $$\hat{O}=\sum_i O_i|O_i\rangle\langle O_i|.$$ How to prove that a convex function $f(\hat O)$ can be expressed like $$f (\hat O)=\sum_i ...
2
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1answer
388 views

How can it be derived that particles described by the Dirac equation must have spin 1/2?

I am reading some lecture notes that unfortunately don't seem to be available online, but that are quite close in spirit in their treatment of the Dirac equation to Sakurai's "Advanced Quantum ...
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0answers
30 views

Corrections in Perturbation theory

Is there a way to construct a bound on the perturbative corrections to a problem in perturbation theory? For example, if I have the standard 1st order correction to the eigensolutions of a problem ...
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1answer
48 views

Hermitian conjugate of an antiunitary transformation

In quantum mechanics, one often considers symmetry transformations which are defined in terms of operators which do not change the norm of states in the Hilbert space. For the Wigner's theorem, this ...
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1answer
41 views

Probability Density of a freely falling body

The following question has been taken from David J Griffith's Intro to QM. This is not my homework! :D Suppose I drop a rock off a cliff of height $h$. As it falls, I snap a million photographs, at ...
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15 views

Repulsive component of intermolecular interaction

Intermolecular interaction mainly consists of 2 components: (a) Dipole vs dipole (permanent & induced), which is more likely to be attractive (b) Pauli exclusion, which is always repulsive The ...
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Are Landau levels always degenerate?

Solving the Landau problem, namely the quantum mechanical problem of a particle in a magnetic field leads to degenerate energy states, the famous Landau levels. My question consists of two parts. ...