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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Prove that $(e^{i\lambda A})^\dagger=e^{-i\lambda A^\dagger}$

Prove $$(e^{i\lambda A})^\dagger=e^{-i\lambda A^\dagger}$$ where $A$ is an operator. Can anyone explain how to go about this question? Writing it as a power series gets confusing. So basically I ...
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10 views

Quantum harmonic ocillator and the mean energy U(T)

The energy of a quantum harmonic oscillator is given by: $$E(n)=\hbar\omega\left(n+\frac{1}{2}\right)$$ The canonical partition function is given by: $$Z(T)=\sum_{n=o}^\infty e^{-\beta ...
2
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1answer
37 views

Can All 4-D column matrices be given as tensor product of 2-D column matrices?

I am familiar with entanglement concept. But it feels bit weird to me that all possibilities of a system in a $4$-dimensional vector space cannot be given as tensor product of two $2$-dimensional ...
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2answers
66 views

What is the correct quantization of Hamiltonians of the form $H=x·p$ whose naive quantization is not Hermitian?

As we all learn in Basic Quantum Mechanics (the first quantization), we promote the classical variables to operators. Say, the classical hamiltonian $\frac{p^2}{2m}+V(x)$ to ...
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23 views

A question on intermediate step in deriving gravitational anomaly by Fujikawa's method

In Fujikawa's 'Path integrals and Quantum Anomalies', Eq.(10.26) in the derivation of gravitational anomaly in Chapter 10.1 is puzzling for me. ...
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Calculating the probability of electrophilic attack on terminal C atoms of butadiene using its wavefunction

I'm studying for a test and came across this question: The highest occupied molecular orbital (HOMO) of butadiene is one of the pi orbitals and it has the coefficients: ...
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1answer
44 views

Difference between quantum numbers j and m and the four others

I am confused about what is the difference between the quantum numbers $j$ and $m$ and the other four quantum numbers: the principal quantum number $n$, angular momentum $m$, etc.? From Quantum ...
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23 views

Charge density of an atomic orbital

Chemistry textbooks on atomic orbitals typically start off with the concept of electrons (viewed as negatively charged point-particles) moving around the nucleus, attracted and bound by the Coulomb ...
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17 views

Photoelectric effect and work function relation

Let's consider the graph above for two metals $M_1$ and $M_2$ showing relation between photocurrent and potential. First question that I want to ask here is that how do you relate stopping ...
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26 views

How to calculate the expectation value of position/momentum using path integrals?

We have the formula: \begin{equation} \langle F \rangle = \frac{\int Dx \times F[\phi] exp\{i/\hbar S[\phi]\}}{\int Dx \times exp\{i/\hbar S[\phi]\}} \end{equation} Now, I am wondering how a change ...
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1answer
51 views

Covariance of the Dirac Equation

i want to show that the following equation holds: $$ \frac{1}{8}\left[\gamma^{\mu},\omega_{\mu \nu} [\gamma^{\mu},\gamma^{\nu} ] \right] = \omega^{\mu}_{~~~\nu}\,~ \gamma^{\nu} $$ $\gamma^{\mu}$ ...
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23 views

Waves and (Another) Question about the Double Slit Experiment [on hold]

Apologies for posting yet another question about the Double Slit Experiment, however, there are a couple of things I wouldn't mind clearing up (if possible!). I don't really have much of a background ...
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31 views

How to calculate the expectation value of position vector?

$$\psi (\vec{x})=Ae^{-(1/4a^2)|\vec{x}-\vec{x}_0|^2}e^{i\vec{p}_0\cdot \vec{x}/\hbar}$$ The wave function is like this, then how is the expectation value of position vector (not position) calculated? ...
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plane wave state used for scattering calculation

When we do scattering calculation off a potential barrier, normally we would assume some incident plane wave and then make use of the boundary conditions. But how is this corresponding to the ...
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1answer
71 views

Quantum anharmonic ocscillator $E_0(\lambda)$ curve or table

I am looking for the exact data on $E_0(\lambda)$ for the anharmonicity $\lambda x^4$. The perturbative expansion is the following: $E_0(\lambda)\approx 0.5(1+1.5\lambda -5.25\lambda ...
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2answers
40 views

One dimensional scattering cross section

My quantum mechanics book (http://www-thphys.physics.ox.ac.uk/people/JamesBinney/qb.pdf, pages 94-95 of the pdf, or 86-87 of the book) considers the one dimensional step potential ...
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53 views

How does light oscillate?

Why do we say that electromagnetic wave is oscillating? Or does light propagate really in a wavy form like this image? What is making the photons oscillate and how is it oscillating is it ...
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20 views

What are the reactions that take place inside battery at the quantum level?

I was just studying about how a battery works on the internet and found out that there are reactions of chemicals which make the electrons move. But what exactly happens inside a battery (lets take a ...
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45 views

Is it possible to make an electromagnetic shield?

Is it possible to make an electromagnetic shield to protect something (or ourselves) against things like bullets, human attacks, metals thrown on us or simple dust particles to protect a spaceship ...
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1answer
65 views

How can we prove this system is in a stationary state?

I'm having trouble using the given hint to solve the problem. The problem statement is as follows: At instant $t=0$, the probability distribution of a particle under a potential $V(x)$ is ...
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1answer
31 views

How to solve infinite square well with exponential solution (of oscillatory type)?

Given a potential well of $V = 0$ on the interval $(0,L)$ and $V = \infty$ outside the well, I am working to solve the Time Independent Schrodinger Equation $$\dfrac{d^2}{dx^2} \psi= ...
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49 views

Can an Atom be negatively as well as positively charged simultaneously?

For example there are three atoms- atom A, atom B, atom C. Atom A has 3 electrons, atom B has 4 electrons and atom C has 2 electrons. If we bring together atom A and atom B, in this case atom A is ...
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28 views

Accuracy of quantum mechanical algorithms

Is it possible for a quantum mechanical algorithm to ensure when the wave function collapses that the right answer will be obtained 100% of the time? For this, I am excluding processes such as ...
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2answers
88 views

The equivalence between Heisenberg and Schroedinger pictures

In quantum mechanics, the two pictures of Schroedinger and Heisenberg are taken as equivalent, where in the former wavefunctions are time variants and operators are not, and in the latter it is the ...
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2answers
66 views

Does a photon travel in all directions?

For example i am standing and a beam of light is passing in front of me. I am able to see that beam of light so does it mean that photons are travelling in all directions other than the photons which ...
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42 views

Is the interference quantum mechanical superposition the same as entanglement? [duplicate]

Are the interference of two wave functions an equivalent way of saying that they are entangled?
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20 views

Orthogonality preservation vs. preparing a state

I'm trying to learn the fundamentals of quantum theory, lately mostly using the lectures by Prof. Susskind which Stanford University made available on Youtube. Here is one thing I have trouble ...
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2answers
81 views

What is the Hermitian adjoint of operator $\hat{K}\psi = \psi^*$?

For many operators, their adjoint can be expressed as a function of other known operators, for example $$\hat{T}_a^\dagger = \hat{T}_{-a} \\ \hat{p}_x^\dagger = \hat{p}_x$$ where $\hat{T}_a \psi (x) = ...
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Valence bond wavefunction of nitrogen

Could someone explain to me how one finds the valence bond wavefunction of an atom? Take nitrogen for example, I know both nitrogen molecules have a valence-electron configuration of 2s22p1x2p1y2p1z ...
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9 views

Stress testing Quantum Uncertainty, a multi Phase Question

I start this line of thinking, and i begin to seek the right questions to ask. I am of humble origin, but even here i remember that all start small somewhere. I think that even the greatest minds ...
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3answers
63 views

What is $E$ in the Planck-Einstein relation?

The Planck-Einstein relation was first given for photons $$E = h\nu$$ But later, de Broglie extended it to matter waves, and showed that it would hold for all particles as well. The $E$ for a photon ...
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1answer
28 views

How to pull out the momentum operator?

In the equation (1.7.17), how does operator $p$ get out of the bracket without any operation though $<a | $, $| x'>$ are function of $x'$? How to prove this?
3
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1answer
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What are these wavish patterns around atoms on microscopic images?

This is an IBM movie about how they move single atoms: http://www.youtube.com/watch?v=oSCX78-8-q0 There are often some "wavish" pattern around atoms on these pictures, like below some of them marked ...
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2answers
76 views

Violation of Pauli Exclusion Principle

From hyperphysics (emphasis mine): Neutron degeneracy is a stellar application of the Pauli Exclusion Principle, as is electron degeneracy. No two neutrons can occupy identical states, even under ...
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1answer
69 views

Why does this resource say that the Schrodinger Equation can be derived? [duplicate]

http://arxiv.org/abs/physics/0610121 If this is true, why do resources say that it cannot be derived? If it isn't true, can someone explain where the above preprint is wrong? I believe that my ...
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1answer
26 views

Is there an implicit assumption that each quantum well contains a single electron only? [on hold]

Is it true that each electron can be represented as a quantum well? I had believed that each energy level was able to contain multiple states and each states were able to hold multiple electrons.
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0answers
29 views

What is the “life time” of a trapped electron?

What does it mean for an electron trapped in a quantum well to have some life time? From the context it sort of times that the electron will move out of this quantum well at some time $\tau$ later. ...
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1answer
37 views

Are The Quantum Assumptions of MBT Theory Correct?

I've become very interested in Tom Campbell's MBT Theory (Plenty of YouTube videos). I can't explain it all here because it takes a book (The one he's written). It's based on the virtual reality ...
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2answers
37 views

Starter's book on Quantum Mechanics (more general and simple books than full QM textbooks) [duplicate]

This question is a little different from other questions referring to books on QM. I ask you to tell me some books that have QM on a simpler level than that of a full course on QM. Some universities ...
12
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3answers
968 views

Why do lines in atomic spectra have thickness? (Bohr's Model)

Consider the atomic spectrum (absorption) of hydrogen. The Bohr's model postulates that there are only certain fixed orbits allowed in the atom. An atom will only be excited to a higher orbit, if ...
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0answers
23 views

Hadamard Gate application help

I need to prove that if you apply Hadamard gates on the input/output before and after a CNOT gate that you get the same answer as flipping the target and control qbits of a CNOT. So for example I'm ...
1
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2answers
51 views

Position space wave function of an electron

In Wikipedia I find the wave function of a free particle to be $$ \Psi(\vec{r},t) = A\,e^{i(\vec{k}\vec{r}-\omega t)}$$ This is is a plane wave moving in the direction of $\vec{k}$ with speed (phase ...
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31 views

Property of helium superfluid [on hold]

I learnt that in helium II every atom would have same wave function and is governed by BE statistics. does that mean all helium II atoms would vibrate in the same way in a field?
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30 views

is there any molecular transition which emits a photon in certain direction

i know molecules having magnetic moment would be aligned in certain direction but do they emit photon in any certain direction when excited? are there any molecules which would emit photon in tthe ...
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1answer
45 views

Representation of operator in “$a$-representation” [on hold]

I have an operator, $X$ say, which is given by a simple phase-shift of the annihilation operator $a.$ I've been asked to give the matrix of $X$ in the $a$-representation, but I was hoping someone ...
2
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1answer
78 views

Singlet state and it's expectation value

So. We have a singlet sate $$ \dfrac{1}{\sqrt{2}}(\vert\uparrow\downarrow\rangle-\vert\downarrow\uparrow\rangle)$$ And two pauli matrices for z axis - one that acts on 1st spin (lets denote it with ...
3
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1answer
66 views

Entanglement ladder algebra and quantization of entanglement

Usually in QFT, even optical quantum mechanics papers, usually resort to describe n-states in terms of the ladder algebra, plus a parameter for polarization, but the entanglement information is ...
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Applicability of perturbation theory

Consider some system in some initial state $|k^{(0)}\rangle$. The probability that such a state makes a transition to some other state $|m^{(0)}\rangle$ can be computed to various orders in time ...
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36 views

Fermion commutation relations QFT question [on hold]

Consider left-handed fermions in two spacetime dimensions $(t,x)$: $\psi_L=\frac{1}{2}(1-\gamma_5)\psi_D$ with $J_0^\epsilon(t,x)=\psi_L^+(x+\epsilon)\psi_L(x-\epsilon)$. (a). Use canonical ...
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Quartic interacion [on hold]

I want to change Lagrangian with coupling constant lambda in quartic interaction so that coupling constant will be negative like in unstable vacuum state. This unstable state I want to describe. Can ...