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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163 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 ...
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1answer
300 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 ...
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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 ...
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5answers
3k 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 ...
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0answers
63 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. ...
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3answers
314 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 ...
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1answer
120 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?
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2answers
248 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 ...
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2answers
215 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 ...
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2answers
2k 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 ...
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1answer
341 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 ...
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0answers
115 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
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1answer
155 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 ...
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2answers
351 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
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2answers
114 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
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1answer
321 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 ...
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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
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1answer
726 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
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1answer
105 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 ...
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1answer
347 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 ...
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1answer
939 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 ...
3
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1answer
342 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 ...
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4answers
201 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.
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1answer
340 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
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0answers
187 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
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2answers
236 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 ...
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1answer
47 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
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1answer
231 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 ...
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0answers
423 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
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2answers
666 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
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0answers
210 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 ...
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1answer
972 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 ...
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2answers
207 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
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1answer
449 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 ...
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3answers
184 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 ...
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1answer
401 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
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1answer
218 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
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2answers
300 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
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2answers
230 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
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3answers
480 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 ...
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1answer
2k 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, ...
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1answer
126 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
138 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
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1answer
110 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 ...
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1answer
140 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
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1answer
119 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 ...
2
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1answer
145 views

Replacing an operator with its expectation value

While dealing with a circling particle in an spherical symetric potential our professor said that we can replace an operator of $z$ component of angular momentum $\hat{L}_z$ with the expectation value ...
2
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0answers
49 views

The role of state space composition in quantum computation

In a paper by Richard Josza and Noah Linden they argue that the way state spaces of composite systems are formed is a key aspect in the benefits of quantum computers. In (classical) phase space, two ...
2
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1answer
745 views

particle density operator in second quantization form

The particle-density operator is given by $n(\mathbf{x})=\sum_{\alpha}\delta^{(3)}(\mathbf{x}-\mathbf{x}_{\alpha})$, then how to derive its representation in terms of creation and annihilation ...
2
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1answer
143 views

Supersymmetry in Quantum Mechanics (Does it apply?)

Suppose we try to apply supersymmetry in quantum mechanics to a particular potential. If you come up with two partner potentials, and two partner Hamiltonians, and then look at the energy of the ...