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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104 views

Does measuring the operator of a wave function collapse the wave function to the measured eigenstate?

Suppose you have a state described by the wave function $\psi(x) = \phi_1(x)+2\phi_2(x)+3\phi_3(x)$ , where the $\phi$s are normalised eigenfunctions of a Hermitian operator $\hat{O}$ with eigenvalues ...
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0answers
65 views

Wave function interaction

If you have two or more wave functions that represent electrons or other charged particles, how would the force on one be calculated based on the charge of the others.
16
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2answers
561 views

Hilbert Space of (quantum) Gauge theory

Since quantum Gauge theory is a quantum mechanical theory, whether someone could explain how to construct and write down the Hilbert Space of quantum Gauge theory with spin-S. (Are there something ...
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1answer
496 views

Why are orthogonal functions and eigenvalues/functions so important in quantum mechanics?

The mathematics and physics we have studied so far at university are heavily focused around the idea of orthogonal functions, orthogonality, sets of solutions, eigenvalues and eigenfunctions. Why ...
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2answers
312 views

Normalising a wavefunction where $\psi$ is equal to a sum of functions [closed]

The wavefunction $\psi(x)$ = $\phi_1(x)$ + $2\phi_2(x)$ + $3\phi_3(x)$ is to be normalised. The functions $\phi_1(x)$, $\phi_2(x)$, $\phi_3(x)$ are normalised eigenfunctions of a Hermitian operator ...
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1answer
329 views

Quantum Mechanics Lx operator [closed]

Show that if the state $ \rvert\gamma\rangle $ is real, then the expectation value of each component of the angular momentum is zero. Does this imply the angular momentum is zero? My Work: $$ ...
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1answer
161 views

Matrix operations on Quantum States in a composite quantum system

Intro (you may skip this if you're an expert, I'm including this for completeness): Say I have two bases for two systems, The first is a spin-1/2 system $|+\rangle = \left(\begin{array}{c} 1\\0 ...
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0answers
96 views

How do we show that photons generated by a constant electric current are distributed according to a Poisson distribution?

I saw the answer sometimes ago in a book "Quantum Electronics" or similar title. I don't remember the author since I lost the book. The book sets ( I believe so ) a constant electric current $I$ in a ...
7
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1answer
417 views

Is it possible to derive Schrodinger equation in this way?

Let's have wave-function $\lvert \psi \rangle$. The full probability is equal to one: $$\langle \Psi\lvert\Psi \rangle = 1.\tag{1}$$ We need to introduce time evolution of $\Psi $; we know it in ...
7
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1answer
127 views

Do systems with level crossings have unstable eigenbases?

It's folklore dating back to von Neumann and Wigner that time-dependent Hamiltonian systems tend not to have level crossings of their energy eigenvalues. However, we can of course consider smoothly ...
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0answers
154 views

Is total angular momentum conserved in particle interaction?

Imagine that two electrons interact by exchanging a virtual photon. I know that the total energy and linear momentum of the two electrons is conserved by the interaction. Is the total (orbital) ...
0
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2answers
111 views

Angular momentum representation

It is well know that, using position representation $$\langle r\lvert L\rvert \psi\rangle =r \times (-i\hbar\nabla\langle r|\psi\rangle )=r \times (-i\hbar\nabla\psi(r)).$$ However, I read ...
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1answer
178 views

Going left or going right of the free particle wave function?

In this excerpt from Griffith's quantum mechanics book: THE FREE PARTICLE We turn next to what should have been the simplest case of all: the free particle [$V(x) = 0$ everywhere]. As you'll ...
3
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0answers
89 views

Solution of QM tasks by using asymptotics

When we solve QM tasks by solving Schrodinger equation, such as tasks about particle in Morse potential, Poschl-Teller potential and many others, we usually find an approximations (lets call them as ...
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2answers
393 views

A few parity questions for simple harmonic oscillator

I think I understand that the solution to the Schrodinger equation for the SHO is based on the Hermite polynomials (and the Guassian function). The solution set of all even Hermite polynomials are a ...
3
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2answers
292 views

Formulation and probability of a wave-function [closed]

I have got this problem where I have been given the following wave function: $$\Psi = 0\quad\text{if}~|x| > a\quad\text{and}\quad A(a^2-x^2)\quad \text{if} \quad |x|< a$$ Now the first question ...
7
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3answers
464 views

Is the uncertainty principle valid?

The uncertainty principle says that the product of the uncertainties in position and momentum can be no smaller than a simple fraction of Planck's constant $h$. Several articles lately suggest this ...
3
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2answers
115 views

Observable Operator on a Superposition?

I'm probably missing something obvious and basic here but I can't make sense of certain usages of Observables as present in basic treatments of Quantum Mechanics that i've come across. $$ ...
7
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1answer
220 views

Quantum version of the Galton Board

If classical particles fall through a Galton Board they pile up in the limit of large numbers like a normal distribution, see e.g. http://mathworld.wolfram.com/GaltonBoard.html What kind of ...
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0answers
62 views

Usage example of stabilizer codes QEC

This question directly follows the previous one about $X$ stabilizers and phase-flip errors: Practical example of stabilizer codes Let's now consider a second part of the quantum circuit that is ...
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1answer
55 views

Pair production at high laser intensity?

Using high laser intensity to produce electron-positron pair, is it still required interaction with nucleus as is the case when gamma rays are used? What causes the pair creation ?
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1answer
162 views

Aren't all electrons the same? So what about electron that absorbs photon?

I learned that electron absorbs a photon and goes into higher energy state. But also all electrons are identical. What is a difference between the electron in low orbital energy state? and the high ...
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0answers
66 views

Faulty Uncertainty Calculations for a Ground State Particle in an Infinite Well

For the infinite well: $$U(x)=\quad\infty : x \leq 0\quad 0 : 0 < x < L\quad \infty : x \geq L$$ $\psi_n=$$\sqrt{\frac{2}{L}}\sin{\frac{n\pi x}{L}}$ Find $\Delta x_n$, the uncertainty in ...
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2answers
737 views

Quantum Commutator Identities

Question: Prove that $p^2$ and ${\bf r}\cdot {\bf p}$ commute with every component of ${\bf L}$ using the identity $$[{\bf p},{\bf e}\cdot {\bf L}]=i\hbar\, ...
2
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2answers
1k views

Proving that the hermitian conjugate of the product of two operators is the product of the two hermitian congugate operators in opposite order

I have reach a step in a problem of my quantum mechanics textbook that requires me to prove the following. $$\hat{A}=(\hat{Q}\hat{R})^{\dagger} = \hat{R}^{\dagger}\hat{Q}^{\dagger}$$ I tried to ...
2
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3answers
103 views

Help with understanding an Operator definition

The operator $\hat{F}$ is defined by $F\psi(x)=\psi(x+a)+\psi(x-a)$ Does this mean $\hat{F}=(x+a)+(x-a)$ and that $\hat{F}$ is operating on $\psi(x)$?
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4answers
388 views

Classical Limit in Quantum Mechanics

Suppose I have a wave function $\Psi$ (which is not an eigenfunction) and a time independent Hamiltonian $\hat{\mathcal{H}}$. Now, If I take the classical limit by taking $\hbar \to 0$ what will ...
1
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1answer
248 views

Heisenberg uncertainty principle - question [closed]

A beam of particles each having mass $m$ and velocity $v$ in the incident on a circular hole of radius $b$ located on a screen. If another screen is placed at a distance $D$ from the hole, ...
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1answer
79 views

Electron in strong magnetic field [closed]

What if we apply a very strong magnetic field to an electron so that it's position be a constant. Then if it's position is constant, it's momentum will also be a constant. But it is in violation of ...
5
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2answers
153 views

Basic Interpretation of Compostion of Observables and their Measurement

Given two (or more) observables $A, B$ which commute one can construct a third observable $C= A \circ B$. If $\psi$ is a common eigenvector of $A, B$ with eigenvalues $\lambda_1, \lambda_2$ then it is ...
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1answer
138 views

Particle Spacing in a Vacuum

Four questions: (To start off, I know very little about physics it isn't even funny (I probably use a ton of wrong terms here and leave out vital information, if so I will try to edit it in as you ...
6
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3answers
209 views

Why are we living in the $q$ part of the phase space?

In Hamilton mechanics and quantum mechanics, $p$ and $q$ are almost symmetric. But in the real world, the $p$ space isn't as intuitive as the $q$ space. For example, We can uniquely identify a person ...
1
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1answer
118 views

Quantum fluctuations and expanding universe

As far as I understand, Hawking radiation is formed at the edge of a black hole, when a particle/anti particle pair is formed and one of the particles falls into the black hole before the particles ...
2
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2answers
152 views

Can the quantum eraser experiment result indicate a 'computed universe'?

The quantum eraser experiment tells us that a photon shot at two slits is a wave, unless you measure which slit is taken and you do not destroy the measurement result. I've found this very similar to ...
2
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3answers
891 views

Why Don't the Ladder Operators Commute?

I have two problems with ladder operators. The first is that I feel they should somehow result in measurable things. The asymmetry of applying the plus operator versus the minus operator is very ...
2
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2answers
1k views

How To Use Ladder Operators?

I'm studying for a test in quantum mechanics and I'm having a hard time understanding how to use ladder operators. There are no examples in my text book, only definitions that I can't understand how ...
2
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3answers
113 views

Curie temperature and magnetization?

If an ferromagnetic object is heated and reaches Tc the magnetization gradually drops as we get closer to Tc or it's a instant drop? Can I assume as I heat the object, the magnetization is weakening ...
14
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6answers
1k views

Why are Only Real Things Measurable?

Why can't we measure imaginary numbers? I mean, we can take the projection of a complex wave to be the "viewable" part, so why are imaginary numbers given this immeasurable descriptor? Namely with ...
4
votes
2answers
179 views

Adjoint of a Wave Function

Why is the adjoint of a function simply it's complex conjugate? Normally with a vector we consider the adjoint to be the transpose (And the conjugate? I don't know why), so does this concept carry ...
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0answers
24 views

quantum mechanics and canonical conjugate [duplicate]

Why nature made conjugates? such as momentum and position, time and energy? Why not energy and position even both do not commute. . thanks in advance
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1answer
248 views

Why is momentum (instead of something else) the canonical conjugate of position?

Why did nature decide to make conjugate of position to be momentum? Since energy and position do not commute, why not energy? What determines the pairing of time with energy and momentum with ...
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0answers
52 views

Adiabatic evolution for initial Hamiltonian on Hadamard basis and problem Hamiltonian as diagonal

This is spawned from a comment at the answer to one of my previous questions. Someone suggested to me that claiming the following statement might be NP-hard. Could anyone please help me to figure out ...
5
votes
1answer
92 views

Classical EM neglects electron recoil?

Imagine two electrons $A$ and $B$ at rest. Electron $B$ is at a vertical distance $r$ above electron $A$. Let us assume that the electrons are constrained to move on horizontal rails. At time $t=0$ ...
1
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1answer
116 views

Normal Coordinates for Quantum Coupled Oscillators

Thanks if you take the time to read this. Here is the problem statement: The problem I'm getting is that I'm not getting the kinetic energy diagonal when I convert to the coordinates that ...
1
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1answer
93 views

Practical example of stabilizer codes

Given the Steane code $$ \left|0\right\rangle_L \equiv \frac{1}{\sqrt{8}}(\left|0000000\right\rangle + \left|1010101\right\rangle + \left|0110011\right\rangle + \left|1100110\right\rangle + ...
1
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1answer
64 views

Confusion about a lemma on the time constraint of an adiabatic evolution (arXiv:quant-ph/0604077)

I am going through the paper Quantum adiabatic evolutions that can't be used to design efficient algorithms by Zhaohui Wei and Mingsheng Ying. On the second page they prove a lemma. The statement goes ...
2
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1answer
138 views

Possible Outcomes from Measuring a Hydrogen Atom

A hydrogen atom is characterized by the wavefunction $$\mid \psi \rangle =\sqrt{\frac{2}{7}}\mid 4\,2\,1\rangle +\sqrt{\frac{1}{7}}\mid 2 \,1\,\bar{1}\rangle+\sqrt{\frac{4}{7}}\mid 3\,2\,0\rangle$$ ...
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0answers
72 views

Angular Momentum with Upper Index

I am asked to show $[L^2,L_i] = 0 $, but with the definition : $L^2 \equiv L_i L^i$ I tried this: $[L_i L^i,L_i] = L_i [L^i,L_i] + [L_i,L_i]L^i$ We know that : $[L_i,L_i]$ = 0 , so we have, $[L_i ...
0
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1answer
95 views

Momentum representation of a function with discontinuous derivative [closed]

Consider the following wave packet $$\psi = Ce^{2\pi i p_0x/h}e^{-|x|/(2\Delta x)}$$ where $h$ is the Planck's constant and $C$ is the normalization constant. The derivative of this function is ...
2
votes
1answer
241 views

Probability current vs. direction of wave function

I did an exercise for my Quantum-Mechanics Lecture: Let $\hbar$=2m=1. A particle in 1 dimension has $j(x)=2\ Im(\overline{\psi} (x) \ \psi'(x))$ and it's to show that there are superpositions $\psi ...