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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39 views

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

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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27 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
36 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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63 views

Modern Quantum Mechanics, Sakurai [closed]

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
91 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
50 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
230 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 ...
0
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1answer
37 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. ...
7
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5answers
814 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
52 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
124 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 ...
1
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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 ...
1
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1answer
50 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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0answers
16 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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0answers
42 views

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. ...
3
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1answer
218 views

The dual role of (anti-)Hermitian operators in quantum mechanics

Hermitian (or anti-Hermitian) operators are of central importance in quantum mechanics in at least two different incarnations: Observables are represented by Hermitian operators on the quantum ...
2
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0answers
65 views

How to get Heisenberg Equation of Motion?

If a system Hamiltonian is given by, $$ ...
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1answer
68 views

Dirac Eqn: why separate operators

At some point Dirac writes: (OpA)(OpB)Y = 0 where OpA and OpB are those two brackets that differ only in the sign of m, then he deduces: (OpA)Y = 0 OR (OpB)Y = 0 (or is that AND). I don't get ...
2
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0answers
46 views

Amplitude for a string to propagate from one point to another

In Zwiebach’s book sections 12.6 and 12.7 interesting aspects of the wave function of the string are discussed. In order to introduce my question first recall what happens with the relativistic ...
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0answers
27 views

Electron wave function seen in Quantum Cascade Laser?

http://sciencequestionswithsurprisinganswers.org/images/qcllevels.gif How did they observe and take a picture of the electron wave function without collapsing it? Does this prove that the wave ...
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1answer
44 views

Relativistic probability amplitude of a particle to be in certain position

In the book “The story of spin” by Tomonaga on page 110, it says They insisted that a concept like "the probability of a particle to be at $x$ in space" is meaningless for relativistic ...
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1answer
57 views

How can i only shine/shoot one proton/electron per second? [duplicate]

I would like to test out the two slit experiment but only one electron or proton at a time.
1
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0answers
80 views

Does Digital Physics imply Heisenberg's Uncertainty Principle? [closed]

I made the following observation which led me to believe that perhaps Digital Physics implies Heisenberg's Uncertainty Principle: Consider Noether's Theorem, which states that space-translation ...
1
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0answers
29 views

Bounds on mixing strength of a quantum channel

Consider a quantum channel $E$ acting on a $d$ dimensional quantum state, with a Kraus representation $E(\rho)= \sum_{j=1}^{k}A_j\rho A^{\dagger}_j$ (where matrices $A_j$ satisfy ...
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3answers
68 views

Born Interpretation of Wave Function

I have just started Griffiths Intro to QM. I was studying Born's interpretation of Wave function and it says that the square of the modulus of the wave function is a measure of the probability of ...
1
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0answers
27 views

What are some of the failed experiments to determine electron's position? [closed]

One that I could think of is trying to observe it with the help of electromagnetic radiation which could tear apart the atom. I asked this because I want to know what sort of methods are used to ...
0
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0answers
43 views

Problems with Dirac's Principles of Quantum Mechenics

I have been having some trouble reading Principles of Quantum Mechanics by P.A.M.D. I think it all burns down into two aspects. 1) In the theory of representations, the notation is awfull when we ...
1
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1answer
79 views

canonical ensemble that is quantum mechanical and continuous?

I do not understand what the following statements from Wikipedia mean For a canonical ensemble that is quantum mechanical and continuous, the canonical partition function is defined as $$ Z = ...
2
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1answer
96 views

Why electron can not be found at some node locations in the infinite potential well?

Consider electron in an infinite potential well, studied in quantum mechanics. Position probability density of the electron is $$ P_n(x)=\left(\frac{2}{L}\right)\sin^2\left(\frac{n\pi x}{L}\right)$$ ...
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2answers
72 views

Postulates of Relativistic Quantum Mechanics

I have been reading this Phys.SE answer in order to clarify my doubts. It seems to me that he claims that the postulates are the same no matter if it is QFT, QM or whatever. But some books tell us ...
0
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1answer
50 views

Would time-dependent wave-functions be constrained by relativity?

Please pardon my beginners understanding. I was thinking about the wave function of a "free particle", $\psi(x,t)$, where $\psi(x,0)$ is the initial condition. Writing $\psi (x,t)$ as $\sum\limits_n ...
5
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1answer
72 views

Delocalization in the square root version of Klein-Gordon equation

In this Wikipedia article a relativistic wave equation is derived using the Hamiltonian $$H=\sqrt{\textbf{p}^2 c^2 + m^2 c^4}$$ Substituting this into the Schrödinger equation gives the square root ...
0
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1answer
20 views

What trajectory do particles follow in the two-slit experiment in Bohm-de Broglie theory

In Bohm de Broglie interpretation of QM particles have trajectories; in the classic two-slit experiment what trajectories do they follow, and how is the interferance pattern interpreted? Are ...
1
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2answers
68 views

Where does the factor of $x$ come from in this formula for expectation value?

Given the normalised ground-state wave-function: $$\Psi(x, t)=\begin{cases} \sqrt\frac{2}{d}\cos(\frac{\pi x}{d})e^\frac{-i\hbar\pi^2t}{2md^2} & \ \lvert x\rvert<\frac{d}{2}, \\ 0 & ...
4
votes
4answers
137 views

Isn't the 'slit' in a double-slit experiment also a wave?

I'm new to QM so excuse my naivety. I was watching an online MIT QM course that described the double-slit experiment (with electrons) when it occurred to me that I have a question. In the video, the ...
0
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1answer
26 views

When does electron capture occur and when does positron emission occur?

I’ve been told that electron capture occurs when there isn’t enough energy to produce a positron by beta plus decay. Exactly why is this the case? Why does it take more energy for positron emission ...
0
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0answers
31 views

Addition of two spins

In the addition of two spins, $S_1$ and $S_2$ show that operators $S_1^2$,$S_2^2$,$S_{1z}$,$S_{2z}$ can have common eigenkets, however, operators $S^2$ and $S_{1z}$ cannot have common eigenkets for ...
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1answer
61 views
+50

Prove that Laughlin's 3-electron states are a complete set of states

In R. B. Laughlin's 1983 Physical Review B article, Quantized motion of three two-dimensional electrons in a strong magnetic field, Laughlin separates out the center of mass motion of the electrons, ...
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0answers
41 views

Why do the quantum numbers take the value they do? [duplicate]

Clearly $n$ can take any positive integer value. But what is the physics and maths behind $l=0,1,...,n-1$ and $m_l=-l,-l+1,...,l-1,l$? i.e. where do these ranges of values come from? (P.S. I know ...
0
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0answers
20 views

Cancelling waves and preservation of energy

In quantum physics, a particle is "defined" by a wavefunction. If you would take 2 particles with the same wavefunction, and negate one of them. They would cancel each other other out. Take for ...
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2answers
69 views

The observer experiment: quantum mechanics

If an observer is needed to see something, but it is an observer that causes a quantum wave function to "collapse" into a classical state, how could we tell that the quantum wave function even existed ...
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4answers
683 views

Is double-slit experiment dependent on rate at which electrons are fired at slit?

I am a mathematician and I am studying string theory. For this purpose I studied quantum theory. After reading Feynman's book in which he described the double-slit experiment (Young's experiment) I ...
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24 views

How is it possible to combine various techniques in cold atom experiments?

I’ve been reading about laser-trapped cold atoms (6Li in particular, which is a fermion) and was amazed at the number of things to keep track of in the experiments, just to gain that degree of control ...