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 ...
1
vote
3answers
47 views
Commutator with a square root
How to find the commutator $[a, \sqrt{a^\dagger a}]$? Here $a$ is a usual bosonic annihilation operator, and $[a, a^\dagger] = 1$.
The first thing I tried is
$$
[x,A] = [x, \sqrt{A}]\sqrt{A} + ...
0
votes
0answers
36 views
Quantum mechanics Perturbation theory
What mathematical condition should be obeyed by a wavefunction which is chosen for perturbation theory in quantum mechanics?
1
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1answer
30 views
No well-defined frequency for a wave packet?
There are similar questions to mine on this site, but not quite what I am asking (I think). The de Broglie relations for energy and momentum
$$ \lambda = \frac{h}{p},
\\
\nu = E/h .$$
equate a ...
-3
votes
2answers
93 views
Consequences of Quantum Mechanics [closed]
First of all, this question is going to seem a a bit of philosophy but know that vague and purposeless wandering is certainly not what i'm trying to propose here.
Also, the reason i didn't post in ...
2
votes
0answers
47 views
Anti-symmetric 2 particle wave function
Suppose we want to construct a wave function for 2 free (relativistic) fermions. As we are dealing with fermions the total wave function has to be antisymmetric under interchange of the coordinates,
...
1
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3answers
87 views
Does entanglement have a speed or is it instantaneous
The phenomenon of observing one entangled particle and noticing the other take on corresponding values... Does this take a finite speed at all or is it instantaneous?
-2
votes
2answers
78 views
Momentum of a particle? [closed]
I really need help to understand what is momentum of a particle (of a photon, proton, an electron...)
I see so many definitions!
My main questions are:
•What exactly is momentum
•What are the ...
11
votes
4answers
245 views
Are the Maxwell equations a correct description of the wave character of photons?
In basic quantum mechanics courses, one describes the evolution of quantum mechanics chronologically. Interference experiments with particles showed that particles should have a wave character; on the ...
2
votes
1answer
38 views
The Molecular Hamiltonian and the avoidance of Overcounting
Whenever I see the total non-relativistic molecular Hamiltonian,
$\hat{H}_{molecular} = \hat{T}_{e} + \hat{T}_{n} + \hat{V}_{ee} + \hat{V}_{nn} + \hat{V}_{en}$
I always notice that the sums ...
6
votes
5answers
175 views
Where did Schrödinger solve the radiating problem of Bohr's model?
One of the problems with Bohr's theory to describe the hydrogen atom, was that the electron orbiting around the nucleus has an acceleration. Therefore it radiates and loses energy, until it would ...
0
votes
1answer
44 views
Question about entangled states
I have a question about entangled state. Suppose I consider the entangled state $\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$. I saw an argument for how measurement of the first bit is affected by ...
2
votes
2answers
53 views
Decomposition of this wave function in eigenfunctions
I have this wave function of a system on a central potential: $V(r)$:
$$\Phi(x,y,z)=C(x+y+z)e^{-\alpha r^2}.$$
And I'm asked a few things about probabilities. I don't have problems with that, because ...
-4
votes
1answer
69 views
Mass conversion to energy [closed]
My teacher asked me to give an example for the 100% conversion of mass to energy. to the molecular level. My answer is "quantum teleportation". Is it right? Are there any other example?
2
votes
2answers
52 views
Are higher order mixed partial derivatives of wave function with different ordination equal?
For example, given two operators:
$$A = \frac{\partial}{\partial x}+\frac{\partial}{\partial y},$$
$$B =\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2} + 1.$$
Deriving commutator ...
2
votes
2answers
49 views
How does the Cern LHC collide particles head on if uncertainty principle limits the precision
I have been wondering why doesn't the uncertainty principle prevent the LHC experiment as if one want to collide two particles together one must accelerate a particle to certain speed and aim it at ...
1
vote
0answers
52 views
Toward the establishment of non-equilibrium (quasi-equilibrium) magnon BEC theory
In 2006, Demokritov et al have reported that they have achieved the observation of quasi-equilibrium magnon Bose-Einstein condensation (BEC) in YIG at finite (room) temperature by using the method ...
0
votes
0answers
14 views
In terms of covariance matrices, are partial measurement and partial trace equivalent?
Partial measurement and partial trace
There is a connection between a measurement of a part of a system and tracing this subsystem out. Say, we have a system composed of subsystems $A$ and $B$ in a ...
1
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0answers
25 views
wavefunction antisymmetry as a limit of a deeper geometric constraint
Recently there was an interesting reformulation of Pauli principle in terms of polytopes: http://physics.aps.org/articles/v6/8
My question is, can this suggest that fermionicity is not a fundamental ...
13
votes
4answers
359 views
Can the photoelectric effect be explained without photons?
Lamb 1969 states,
A misconception which most physicists acquire in their formative years is that the photoelectric effect requires the quantization of the electromagnetic field for its ...
1
vote
0answers
48 views
How to absorb a characteristic line in a spectrum
I have an x-ray tube. When I see the spectrum, I notice the characteristic lines of the anode. What do I have to do if I want to absorb a characteristic line?
I have thought that I can add a filter. ...
-5
votes
3answers
43 views
What made up light photons? [duplicate]
mass is energy per c square $m=E/c^2$ energy is made up of photons but what made up photon itself?
what made up a single photon?
Replay to comment:
but as we can see in history early phyisicists ...
1
vote
1answer
52 views
Is light particle of wave?
We know that Young's double slit experiment shows that light is a wave.
On the other hand photoelectric effect shows that light is made up of photons.
How can light be both at the same time?
4
votes
1answer
83 views
Examples of “pseudo quantum effects” in history of physics
Are there any examples in the history of physics where a phenomenon was considered by the physics community to be not explainable by classical physics and needed a quantum explanation whereas some ...
1
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1answer
85 views
+50
Energy time complementarity from unitary evolution
I am looking for a well posed experimental situation that illustrates energy time complementarity. I know of Einsteins box, which is discussed quite nicely in Bohr's article Discussions with Einstein ...
-5
votes
2answers
93 views
Does shadow have mass?
I know it sounds like a foolish question but I have a reason for asking and I'm hoping someone here, can give a convincing response.
Here is why I pose the question...it seems to me that all this ...
-1
votes
1answer
57 views
Problem from Sakurai about a delta-function potential [closed]
Can you help me with this problem from Sakurai:
A particle of mass m in one dimension is bound to a fixed center by an attractive delta-function potential:
$$V(x) ~= ~-a\delta(x) , \qquad ...
1
vote
0answers
67 views
How to understand the matrix behind a Hamiltonian?
thanks to the answers I received to my previous questions, I could derive correctly an elegant partition function for my problem which resembles a second quantized model taking the particles to be ...
2
votes
1answer
48 views
when is coherent state a good approximation?
Consider a Hamiltonian of a system coupled to a bath. Let $H_{sys}=\nu c^{\dagger}c$ ; $H_{env}=\Sigma \omega_r a^{\dagger}a$ ; $H_{int}=\Sigma (g_r ac^{\dagger}+g_r^* ca^{\dagger})$. Then it is ...
2
votes
2answers
76 views
Obtaining an expression for the Lorentz Force in the Dirac theory [duplicate]
We know that $P = p - \frac{e}{c} A$
How can we obtain a expression for the Lorentz force from the equation above using the Dirac Theory??
Could you please explain this to me step by step?
The only ...
6
votes
2answers
59 views
Neutral pions and chromodynamics
$\pi^0$ particles are either up-antiup or down-antidown (or strange-antistrange?) They must be opposite colors to preserve neutrality. Why don't the opposite quarks annihilate?
0
votes
0answers
29 views
Diffraction grating efficiency in terms of QM
I am working with trying to find diffraction efficiencies of multilayered coatings. I am not a huge fan of getting into the tensor calculus most of the papers (Li, Chandezon) address, so I was ...
4
votes
1answer
44 views
Is the number-phase uncertainty relation classical?
For a harmonic oscillator in one dimension, there is an uncertainty relation between the number of quanta $n$ and the phase of the oscillation $\phi$. There are all kinds of technical complications ...
-3
votes
0answers
45 views
How strong is the strong force? [duplicate]
What is the strength of the strong force between, for instance, a proton and a neutron separated by a distance on the order of femtometers? If a concise answer is impossible to formulate, what is an ...
1
vote
0answers
35 views
Ascertaining a mathematical equality to derive a partition function
we have an equation like this:
$$\mathcal N(x)=\sum_{q=1}^\infty (\psi(x,q) \log(q)) \qquad (1)$$
while $\psi(x)$ is the function for some oscillations (may contain complex part), $x\in \Bbb R$ and ...
2
votes
1answer
33 views
Parity of spin states
Since orbital angular momentum commutes with the parity operator and since both are hermitian it is possible to build a common basis. These are the spherical harmonics, whose parity is known.
Now, ...
4
votes
1answer
36 views
Limits of superdense coding
Holevo's theorem says that no more than n bits can be stored (and retrieved) in n qubits. Indeed, allowing error can't improve this either -- the probability of retrieving the correct information is ...
-1
votes
0answers
32 views
Possible outcomes of measurement on a state
I having some trouble understand a question I'm handed. I doesn't seem to be difficult, I think, but I'm having some trouble understanding what I actually have to do.
I have the following variable ...
0
votes
1answer
52 views
Showing Dirac Hamiltonian is hermitian
I'm trying to show that $H_D = -i\boldsymbol{\alpha}.\nabla+\beta m$ is hermitian.
Its given that
$$
\gamma^{0\dagger}=\gamma^0
$$
$$
\boldsymbol\gamma^\dagger=-\boldsymbol\gamma
$$
What i've done ...
2
votes
1answer
35 views
Probability for harmonic oscillator outside the classical region
I'm having some trouble finding an expression for the probability to find the particle outside the classical area in the harmonic oscillator.
I have a wavefunction defined as:
$\psi \left( x,\,t ...
2
votes
1answer
65 views
Measuring Entangled Qubits
Suppose we have a pair of entangled qubits.
$$
|\psi\rangle = \frac{1}{ \sqrt{2} } ( |00\rangle + |11\rangle )
$$
Now we give one qubit to Alice and other to Bob. Alice measure the her qubit to ...
3
votes
4answers
123 views
Quantum Collapse
When we observe a quantum object does it collapse into a point? Or does it collapse into a smaller wave of area that is out of our range of accuracy? My gut tells me the latter.
1
vote
1answer
40 views
Average force and pressure in a 3D box due to quantum non-interacting particles
A gas of non-interacting quantum particles occupies a box with lengths $L_1, L_2, L_3$. Calculate its energy and thus the average force and pressure exerted by the gas on the walls of the box.
I have ...
-3
votes
0answers
54 views
Raising/Lowering Operator [closed]
The question asks; For a harmonic oscillator,
$$
\langle2|a_{-}\,a_{+}^{3}|0\rangle
$$
which equals...
And there are numerous multiple choice answers. I calculated $$2\sqrt3$$ but the answer sheet ...
3
votes
0answers
90 views
The Hamiltonian for clocks?
I am rather a theoretician and looking for a formalism to represent biological clocks by Hermitian operators.
The simplest thought model I am looking for is a formal representation of a clock (for ...
1
vote
3answers
102 views
Is everything pre-decided? [closed]
"There is nowhere in the universe where the laws of physics are violated." Considering this general to be true,can i conclude that everything is pre-decided? I can explain this in the following ...
1
vote
1answer
37 views
Charge in terms of wavefunctions
For a charged quantum particle, say, an electron or a quark, how in the particle's wavefunction is the electric charge represented? Is it truly possible to represent electric charge using the wave ...
5
votes
1answer
67 views
Photons: Collection of Wave Packets that produce a plane wave
Is it possible mathematically for photons, which behave as individual Gaussian wave packets, to combine in such a way that the approximate result is a plane wave at one particular frequency (i.e., the ...
4
votes
2answers
172 views
Spin - where does it come from?
I study physics and am attending a course on quantum field theory. It is hard for me to draw connections from there to the old conventional theories.
In quantum field theory spin originates from the ...
3
votes
0answers
50 views
How is the Geometric Phase measured in the experiment?
I had read some papers that have mentioned the geometric phase (Berry phase) can be used to detect the quantum phase transitions in a quantum many-body system. My question is: How is it measured in ...
0
votes
1answer
70 views
Expectation value of momentum
I'm having a problem with an expectation value that doesn't seem to add up for me.
What I know is, that $\psi(\vec{r})$ is a wavefunction for a particle in three dimensions. The Hamiltonian is given ...
