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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3answers
4k views

Adding 3 electron spins

I've learned how to add two 1/2-spins, which you can do with C-G-coefficients. There are 4 states (one singlet, three triplet states). States are symmetric or antisymmetric and the quantum numbers ...
0
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1answer
22 views

The minimum possible energy for five noniteracting spin $\frac{1}{2}$ particles

Question What is the minimum possible energy for five (noniteracting) spin $\frac{1}{2}$ particles of mass $m$ in a one-dimensional box of length $L$? Answer: $$ 2 \times ...
1
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3answers
36 views

Calculating the probability of a given energy

Given a normalised wavefunction say $$\psi(x) = A\sin(n\pi x),$$ (where $A$ is a normalisation constant) I can calculate the probability of finding the particle being between a position $x$ and $x + ...
2
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1answer
23 views

Sequential Stern-Gerlach Experiments

Suppose a beam of particles is prepared with spin in the $+z$ direction (e.g. by a Stern-Gerlach apparatus). Suppose this beam then enters a Stern-Gerlach apparatus with orientation $\theta$ relative ...
1
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1answer
84 views

Difference in partition function of classical and quantum Ideal gas

First, I have read this question:What is meant by the term "single particle state" There is an analysis going on in my book (Mandle F. Statistical Physics) that has brought me in a ...
-3
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1answer
48 views

How do I normalize this wavefunction? [on hold]

I need to find the normalisation constant $A$ for the wave function: $$ \psi\left(x\right) = \left\{ \begin{array}{lr} A &\: \frac{-a}{4} \leq x \leq \frac{a}{4}\\ 0 &\: ...
-1
votes
1answer
33 views

Time dependent solution to infinite well

A particle of mass $m$ is confined within an infinite, one-dimensional potential well, $U(x)$, of width $a$. $$ U\left(x\right) = \left\{ \begin{array}{lr} \infty &\: x \leq ...
1
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2answers
157 views
+50

Estimating our de Broglie wavelength

This could be a very naive question, but I feel always disturbed by it since I couldn't ever figure out a perfect answer. Why is our de Broglie wavelength (dBw) so tiny and how could we roughly ...
2
votes
2answers
150 views

What counts as information?

What counts as information? In e.g. the EPR experiment why is one entangled particle knowing instantaneously the state of the other not counted as 'information'.
3
votes
1answer
193 views

First order coherence through double slit

The state $$|\Psi \rangle = |0\rangle + \sum_j \int d\omega f_j(\omega)\hat{a}^\dagger_j (\omega) |0\rangle $$ is coming from a far field and incident on a double slit setup. Here j is the index of ...
2
votes
4answers
145 views

Physical reason why the derivative of a wavefunction has to be continuous?

Question What is the physical reason (i.e. without any maths) that the derivative of a wavefunction (except with infinite potentials) has to be continuous? Other info I know that in the classical ...
0
votes
1answer
47 views

Getting to spins of arbitrary direction

Let me rephrase this question: Let us assume we know that symmetry transformations always look like this: $$U(s)=e^{iKs} $$ with a hermitian Operator K. This tells us that for very small $s$: ...
0
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1answer
20 views

Does the electron confinement energy vary with temperature?

I was introduced the electron confinement energy. At room temperature thermal energy of a particle is about $k_B T$, where $T=298K$, giving about $25meV$. I was told that $E_\text{confinement}=50emV$, ...
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votes
0answers
10 views

What is the energy levels of 1d hydrogen by using WKB?

I need to find the energy levels of 1d hydrogen using WKB and $V(x)=-1/x$? can you help me please?
3
votes
2answers
110 views

What really is a particle?

In Classical Mechanics we consider particles as things whose internal structure for the purpose of studying some phenomenon might be neglected. In that setting we associate particles to points and ...
0
votes
1answer
32 views

Acceleration of uncharged particles

Following on from this comment - do uncharged particles radiate under acceleration? (no offense to the commenter, just clarifying as I've not heard of this before) Why is this? I vaguely recall a ...
0
votes
0answers
37 views

Photograph of Light as Wave and Particle [duplicate]

what is this? actually its the first photo of light as wave and a particle. The bottom "slice" of the image shows the particles, while the top image shows light as a wave. i have questions 1.how ...
9
votes
1answer
179 views

Do Franck-Condon oscillations have natural lineshapes?

I recently found a paper (for the curious, this one) that talks about observing the motion of a nuclear wavepacket in H2O, as initiated by tunnel ionization. This wavepacket should be thought of as a ...
0
votes
2answers
48 views

'schrodinger' picture in measurement based topological quantum computation

I am looking at the measurement processes in topological quantum computation (TQC) as mentioned here http://arxiv.org/abs/1210.7929 and in other measurement based TQC papers. Let's say I start with ...
5
votes
2answers
980 views

Is it guaranteed that wavefunction is well behaved everywhere?

I don't really know much about Quantum mechanics, but would like to know one simple fact. The state function $\Psi(r, t)$ whose magnitude gives the probability density of the position of the particle ...
1
vote
1answer
50 views

How might I show that an operator is, by definition, an 'observable'? [on hold]

Here is my problem: I understand what is meant by 'observable' but don't have a formal definition at hand. How do I 'show' it?
3
votes
1answer
73 views

Electron momentum distribution and wavefunction in momentum space

Does there exist any relationship between the electron momentum distribution used in above threshold ionization and the wave function in momentum space? In other words, starting with the wavefunction ...
-5
votes
0answers
28 views

Posibility of time travel/multiple realities/time phase shifting [on hold]

Sounds odd and unlikely, but let me explain the situation. Going on the de ja vue ideal, which we probably have all experienced, I believe things of such a matter are possible. Just today when I ...
2
votes
1answer
54 views

Number of Nodes in energy eigenstates

I have a question from the very basics of Quantum Mechanics.Given this theorem: For the discrete bound-state spectrum of a one-dimensional potential let the allowed energies be $E_1<E_2< ...
1
vote
2answers
75 views

Have two identical quantum mechanical experiments ever been done?

Have two experiments ever been done such that the set up is identically the same, (when I say identically I mean down to the atomic level). Of course the experiment would have to be very simple. If it ...
6
votes
4answers
141 views

Does quantum mechanics imply that particles have no trajectories?

In Classical Mechanics we describe the evolution of a particle giving its trajectory. This is quite natural because it seems a particle must be somewhere and must have some state of motion. In Quantum ...
6
votes
1answer
219 views

Is WKB really applicable for the ground state?

It seems that WKB is applicable for a given $E$ if and only if $\hbar$ is sufficiently small. Or in other words, WKB is applicable if and only if the quantum number is large enough. Is this ...
0
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2answers
31 views

A binary operator required for observing whether the particle is present in a given spatial region

Consider the wave function $\psi(x)$, I want to define an experiment using quantum mechanical rules. The experiment is to find whether the particle is in the region of space (a,b). The observable is ...
1
vote
2answers
88 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 ...
13
votes
1answer
445 views

How to evaluate this sum of coupling coefficients?

I would like to evaluate the following summation of Clebsch-Gordan and Wigner 6-j symbols in closed form: $$\sum_{l,m} C_{l_2,m_2,l_1,m_1}^{l,m} C_{\lambda_2,\mu_2,\lambda_1,\mu_1}^{l,m} \left\{ ...
1
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0answers
33 views

What is the relationship between coherent states and quantum coherence?

What is the relationship between coherent states and quantum coherence? To me coherent states were only talked about in regard to Quantum Harmonic Oscillator, whereas coherence and decoherence on the ...
0
votes
0answers
28 views

Why we compare expectations sometimes and sometimes probabilities?

I am reading device independent approach on quantum mechanics from here device independent outlook on quantum mechanics. In here the author introduces local variable theory. Then he give two results. ...
1
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0answers
39 views

Scattering amplitude, link between quantum mechanics and QFT

In quantum mechanics, we can define the scattering amplitude $f_k(\theta)$ for two particles as the magnitude of an outgoing spherical wave. More precisely, the asymptotic behaviour (when ...
3
votes
2answers
113 views

Why does the magnitude squared of the wave function give us the probability density? [duplicate]

My question doesn't go much beyond the title: Why does $$\left | \psi \left ( x,t \right ) \right |^{2}$$ give us the probability density of something appearing at a certain location? I understand ...
0
votes
0answers
56 views

Does EPR permit information to travel faster than light? [duplicate]

This question always throws me: Discuss if the EPR paradox violates special relativity? The information of the state of one particle is instantaneously transmitted to the other particle, but ...
4
votes
1answer
237 views

Do Bell inequality violations appear instantly when the source is turned on, or do they increase over time?

This experimental Question is a result of reading a particular article on Bell violations. I addressed the e-mail below to the corresponding authors —because who knows, they might reply— but it is not ...
6
votes
1answer
119 views
+50

Why schmidt decomposition only holds for two component composite systems?

According to schmidt decomposition any pure state belonging to a composite system $AB$ can be written as $|\psi\rangle = \sum_i \lambda_i |i_A\rangle |i_B\rangle$ where $\lambda_i$ are non negative ...
4
votes
2answers
123 views

If proton spin emergence from quarks and gluons is mysterious, why is silver atom spin not?

A recent Scientific American article brought up an old issue, which is this: According to quantum chromodynamic models, the emergence of exactly 1/2 unit of spin in a proton (or a neutron, or any ...
0
votes
0answers
17 views

Hadron Annihilation - what happens with the constituents

When a Hadron and its antimatter equivalent annihilate, what happens to the QCD "soup" (for lack of an appropriate term) from each? Eg, the valence quarks in a proton - antiproton event, to they pair ...
6
votes
2answers
108 views

Do bras and kets have dimensions?

I'm trying to understand more intuitively what bras and kets are, but some aspects of them remain a mystery to me. We usually think of $\psi (x)$ as having dimension of $[1/\sqrt{L}]$ so that ...
1
vote
0answers
18 views

symmetry group of multi-electron atom

Neglecting spin effects, the energy levels of multi-electron atoms are characterized by states of definite total orbital ($L^2$) and spin angular momentum ($S^2$). From this it seems that the ...
4
votes
2answers
94 views

How is CNOT operation realized physically?

I think I understood very well how operations on one qubit are done - if qubit is electron, we just apply magnetic field in direction we want to make spin precess (unitary operations on single qubit). ...
2
votes
3answers
95 views

What can change a photon's frequency?

I found this question: Is it possible to apply force to a light particle? As it states, gravity can change the frequency of light by changing its momentum. My question regards other phenomena that ...
0
votes
2answers
48 views

derivation qm canonical ensemble

In classical mechanics the canonical ensemble can be derived from the microcanonical ensemble of two systems in weak interaction. Is a similar thing possible in quantum mechanics? Is there any good ...
1
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1answer
40 views

Uncertainty relation and instrumental errors

I was puzzled recently by what I've read in the internets about Heisenberg's uncertainty principle (one probably should never do this). It claimed that in the usual relation $$ ...
0
votes
1answer
48 views

Can someone explain what's the difference between all these terms in “Simple Words” with their “applications”? [on hold]

I'm very confused between all these terms. Can someone explain what's the difference between Classical Mechanics, Relativistic Mechanics, Quantum Mechanics, Quantum Field Theory, ...
1
vote
1answer
17 views

Franck-Hertz experiment what transition takes place?

For the Franck-Hertz experiment there is a voltage drop at $4.9\rm\,V$. What transition does this represent in the mercury? Looking at the energy levels it seems to be from the ground to the 2nd ...
0
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0answers
40 views

How is a measurement on an electron done?

There are two ways how to change a direction of a qubit - one with Larmor precession, another with a measurement. I am not sure about the measurement one. Let's say I have an electron with spin ...
0
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0answers
15 views

Infinite bare quantities and dressed quantities confusion

I'm getting very confused. Taking the example of the mass of the Z-boson. Constructing the GWS model using gauge symmetry breaking one finds a lagrangian which is a function of the Z-boson mass: ...
1
vote
1answer
46 views

Example for System Given Hilbert Space

What are some concrete examples of physical systems such that their corresponding Hilbert space is given by $\mathbb{C}$? Also, what is the physical difference between a system whose corresponding ...