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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8answers
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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
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1answer
86 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
152 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 ...
2
votes
2answers
136 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 ...
1
vote
2answers
131 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
1answer
221 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 ...
2
votes
0answers
47 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 ...
21
votes
4answers
2k 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
59 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. ...
-4
votes
3answers
197 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 ...
-2
votes
1answer
99 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?
6
votes
2answers
241 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 ...
5
votes
2answers
206 views

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 ...
-6
votes
2answers
1k views

Does shadow have mass? [closed]

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
247 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
110 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
127 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
270 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 ...
5
votes
2answers
105 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?
4
votes
1answer
235 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 ...
1
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0answers
46 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 ...
3
votes
1answer
436 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
76 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 ...
0
votes
1answer
268 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
691 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
239 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
180 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
274 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
181 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 ...
2
votes
2answers
196 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
45 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
182 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 ...
0
votes
0answers
311 views

Is it theoretically possible for a person to pass through a solid wall/object?

I understand that matter cannot pass through other solid matter because of the electrons that orbit an atom prevents this but I was curious to know if it is theoretically possible to somehow get ...
9
votes
2answers
513 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
169 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
787 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 ...
0
votes
2answers
183 views

Can deterministic world view be denied by anything other than quantum mechanics

If we ignored quantum mechanics and looked at the world with a deterministic Newtonian view. Does not that mean that there is no randomness and that if all the information of the state of the universe ...
5
votes
1answer
350 views

What do up-left orthogonality has in common with up-down and what is their relationship?

I am familiar with the true (or general) notion of orthogonality, given in the Linear Algebra and Pythagoras theorem derived from the $\vec x \cdot \vec y = 0$. I have also recently got to know that ...
0
votes
3answers
177 views

What is the name of the equation which led to the Schrödinger one?

What is the name of this equation: $$\frac {d^2\psi}{dr^2}+k^2\psi=0?$$ (I want a Wikipedia link for this equation, but I don't know what its name is.) Point: In this equation, the wave function ...
2
votes
1answer
337 views

Why doesn't Ehrenfest's theorem work for a particle in a an infinite square well?

I'm reading Griffith's Intro to Quantum Mechanics, and he mentions that in an infinite potential well, a classical particle would simply bounce back and forth between the two walls indefinitely. He ...
5
votes
1answer
195 views

Aharonov-Bohm Effect in Torus

I had a very brief introduction to the Aharonov-Bohm effect in class. The lecturer introduced the notion that $H(\Phi=\Phi_0)$ and $H(\Phi=0)$ gives identical energy spectrum and that the Hamiltonians ...
3
votes
2answers
208 views

Composition of squeeze operators?

I'm wondering if it exists a composition law for the squeezing operation ? I guess so for geometric reason, since they are (generalized, and the phase is annoying of course) hyperbolic rotations of ...
2
votes
2answers
227 views

Text interpretation in Griffith's intro to QM

It says in Griffith's chapter 2.1, that: $$\tag{2.14} \Psi(x,t)~=~\sum_{n=1}^{\infty}c_n\,\psi_n(x) e^{(-iE_n t/\hbar)}$$ It so happens that every solution to the (time-dependent) Schrodinger ...
3
votes
3answers
402 views

Classical/Quantum Coin Toss

I am having a brainfreeze moment and have confused myself, help appreciated! Classical Coin: Heads OR tails. Quantum Coin: Superposition Heads AND Tails. Classical Mechanics: Deterministic (in ...
0
votes
1answer
1k views

Expectation value of position in infinite square well

I'm looking for some help to a question. I'm working in the infinite square well, and I have the wavefunction: $$\psi(x,t=0)=A\left( i\sqrt{2}\phi_{1}+\sqrt{3}\phi_{2} \right).$$ For every time t, ...
-3
votes
1answer
99 views

Superposition and the Winning Jackpot Numbers

Let's say I buy myself a lottery ticket (Mega-Millions). I have $\frac{1}{175,711,536}$ chance of winning. Before I tune on the tv/radio and listen to the winning numbers (i.e. make an observation), ...
2
votes
1answer
124 views

How do I find the energy of this Hamiltonian?

So, I have a (confusing) Hamiltonian: $$H = \int \mathrm{d}k\,\omega_{k} a^{\dagger}\bigl(\vec{k}\bigr)a\bigl(\vec{k}\bigr)$$ where $\omega_{k} = \sqrt{k^{2} + m^{2}}$ and the measure is ...
4
votes
1answer
103 views

Using angular momentum in complex coordinates

So given the angular momentum operator: $$L_{z} = - ih\biggl(x \frac{\mathrm{d}}{\mathrm{d}y} - y \frac{\mathrm{d}}{\mathrm{d}x}\biggr)$$ I know how to write these in terms of polar coordinates ...
0
votes
1answer
132 views

A question about quantum measurement and associating a linear self adjoint operator to it

I have a question about the concept of measurement and observable in quantum mechanics. I'd like to fist explain my understanding of it and then ask the question. First we have a system and its ...
4
votes
1answer
108 views

Canonical / Grand-Canonical average annihilation operator

Does anyone knows a simple way to understand why the average value of the creation (or annihilation) operator should be equal to zero in the Canonical Ensemble? Why instead if I'm dealing with a ...