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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Creation and Annihilation Operators

Let $\widehat{a}^{+}_{i}$ and $\widehat{a}_{i}$ be the usual bosonic creation and annihilation operators. Consider $$\widehat{q}_{i} = \sqrt{\frac{\hbar}{2m_{i}w_{i}}}(\widehat{a}_{i}+ ...
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Quantum mechanics threshold

First of all I beg your forgiveness as I am not a physicist and the question I am going to ask may sound silly. I am aware that beyond a certain threshold in the hierarchy of building blocks of ...
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Formation of atoms question

Could you please, explain to me the logic of the folllowing process as you would do to your 8 y/o sister: Ubiquitousness and stability of atoms relies on their binding energy, which means that ...
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What is a measurement in MWI

I was reviewing the MWI, and couldn't figure what a measurement is in the MWI? Everett claims that split happens when you measure, but what is it for MWI (not for general QM)? Yes, I know about ...
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34 views

Probability to be in a particular state

If I have a wavefunction $\psi = \sum_{n=0}^{\infty} a_n e^{i \phi_n} | n \rangle$ and $(|n \rangle)$ is a set of orthonormal functions. Is it correct that the probability to be in a state $|k\rangle ...
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Uncertainty relation for a photon [closed]

Is it possible to derive an uncertainty relation (Karolyhazy Uncertainty: http://dx.doi.org/10.1007/BF02717926) with photons? I brainstormed a bit to get the following: $$ \Delta x_0 \Delta p_0 = ...
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Two-Electron System

I'm reading the section "Two Electron System" in Sakurai's textbook and I'm stuck on the following reasoning: Let us now consider specifically a two-electron system. The eigenvalue of the ...
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How can I write a Gaussian state as a squeezed, displaced thermal state

I would like to write a Gaussian state with density matrix $\rho$ (single mode) as a squeezed, displaced thermal state: \begin{gather} \rho = \hat{S}(\zeta) \hat{D}(\alpha) \rho_{\bar{n}} ...
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How can we say that a wave function follows schrodinger equation using operators?

If I have an operator which has an eigenfunction which follows schrödinger's time-dependent equation , and I have another eigenfunction to this operator , can I say that even the other eigenfunction ...
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Asymptotics of the Wigner 6j Symbol

So, in doing some numerical computations in QFT, I've run into the following Wigner 6j-Symbol: $ \left\{ \begin{array}{ccc} x & J_1 & J_2 \\ \frac{N}{2} & \frac{N}{2} & \frac{N}{2} ...
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Was Max Born the first to notice a connection between quantum mechanics and randomness?

Max Born introduced the Born Rule in a paper from 1926. But was this really the first time that a connection between quantum mechanics and randomness was noticed? Today, quantum mechanics and ...
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QM interpretations

I don't fully appreciate what the discovery of the decoherence phenomenon adds to the Copenaghen interpretation of QM. I will be more precise: the Copenaghen interpretation, if I am not wrong, is ...
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Approach to expressing $|n\rangle\langle n| $ as a polynomial when eigenvalues are degenerate?

If ${|n\rangle}$ are eigenvectors of an operator $A$ then $|n\rangle\langle n| $ can be expressed in terms of a finite order polynomial $$|n\rangle\langle n| =\prod_{m\ne n} \frac{A-a_m}{a_n-a_m}$$ ...
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Dependence of sign on operators in wave equation?

In the time-dependent Schrödinger equation, our teacher told us about energy and momentum operators. He just defined them, the equation was of the form $A\exp(i(kx-\omega t))$, if we take the ...
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34 views

Thought Experiment: Force on magnets in a Stern Gerlach Experiment

Background: In the SG experiment, an inhomogenous magnetic field affects a force on particles passing between two magnets. "Measurement" takes place when a screen is placed on one end, blocking one ...
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57 views

Negative Solution for Dirac Equation

The negative solution for the Dirac equation predicted the existence of positron. Can anyone show that basic solution for this?
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Does the superposition principle affect the space of quantum states?

I am confused about the set of quantum states. I have seen it written that in classical physics, the set of all states is a simplex. (I think this refers to the probability simplex.) In quantum ...
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Are double-slit patterns really due to wave-like interference?

According to various sources on the web, it seems like the general concensus is that there isn't actually any wave-particle duality with quantum particles. For example, this article implies that ...
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34 views

The triangle inequality in CHSH derivation, where is the triangle?

http://en.wikipedia.org/wiki/CHSH_inequality#Bell.27s_1971_derivation ... |X + Y| <= |X| + |Y| ??? CHSH inequality is combined from four relative angles between four polarization axis which do ...
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How hot particles can get [duplicate]

One way in which an object is affected by temperature rise is that the wavelength of the radiation it emits is gets smaller and smaller. Another way of looking at it is that as an object gets hotter, ...
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What's the value of the coupling constant in interacting field theories?

Consider this Lagrangian : $L = \frac{1}{2}(\partial_\mu \Phi)^2 - \frac{M^2}{2}\Phi^2 +\frac{1}{2}(\partial_\mu \phi)^2 -\frac{m^2}{2} \phi^2 -\mu\Phi\phi^2$ Its interaction term is given by : ...
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Questions on quantum mechanics [closed]

First Question I have problem with little alternative form of Dirac equation. This problem refer to a matrix $\alpha$ in this equation. I mean detailed general contravariant form of equation in which ...
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Am I missing a trick to solving this differential equation?

I was playing around with a 3-D potential $V$ such that $V_{(r)} = 0$ for $r<a$, and $V_{(r)} = V_0$ otherwise. By using the Schrödinger Equation, I showed that: ...
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86 views

Does one really need classical physics in order to understand quantum physics? [closed]

I want to start studying quantum mechanics, and then move to quantum field theory. I have a strong mathematical background, and I think this aspect of quantum physics won't be a problem to me. Though, ...
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How to measure the pressure on the walls of a potential box by a particle inside?

Consider a quantum particle inside a 3D potential box. One can compute the pressure that it exerts on the walls, it's OK. But what puzzles me is how do we actually measure such a pressure? If we take ...
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Question about electromagnetic Spectrum [closed]

I have question related to electromagnetic Spectrum. If energy of photon is $E=m_e c^2$, to which part of the electromagnetic spectrum does it belong ?
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Square of the Pauli matrices and the identity matrix

The square of any of the three Pauli Spin matrices is equal to the identity. Is there any physical meaning to this? Would you expect it? Maybe in the context of the $SU(2)$ group?
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Blackbody radiation through quantum mechanics perspective

While explaining black body radiation, the body is assumed as a cavity radiator and the radiations are due to the oscillating electrons. But we know that the electromagnetic radiation emitted is ...
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Copenhagen interpretation

Reading some science history, Werner Heisenberg and Bohr created the Copenhagen interpretation, but what I didn't get is how can we connect this interpretation to Schroedinger's cat and the double ...
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106 views

Tensor Product of a Bra and a Ket

What does one get if the take the tensor product of a bra and a ket, for instance, $\langle\uparrow \rvert \otimes \lvert \downarrow\rangle$? What I mean it, what is this object? What does it act on? ...
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70 views

Total Angular Momentum of a Hydrogen Atom

Griffiths in his celebrated book named 'Introduction to Quantum Mechanics' discusses about the total angular momentum of a hydrogen atom on page 187. He writes: If a hydrogen atom is in the ...
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138 views

What is the physical reason behind linearity of Schrodinger's equation?

What is the physical reason for Schrodinger equation to be linear? Though in physics many interactions or dynamics are found non linear.
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Do small-scale physical effects lead to larger systems being required for long life (of dynamic systems, not static objects)

I think physicists can deal with this question best. I answered a question about "immortality" when some guy claimed I got it wrong that neurons die (I argued that even if you live a billion years ...
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A new way of looking and formulation of Observables for a new quantum theory

I often think of basic of QM (although it wasnt discovered that way) is that we have a physical parameter/observable and the favourite one is the displacement $x$ of a particle $P$. Its conjugate ...
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Different mathematical methods in quantum mechanics?

My understanding is that in quantum mechanics the wavefunction may be expressed as a function or as a ket vector (composed of many orthogonal ket vectors). I'm not too sure about the further ...
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How to find optical toy models of entangled quantum mechanical systems?

I recently read Arnold Neumaier's lectures on uncovering classical aspects of quantum mechanics: Classical and quantum field aspects of light Optical models for quantum mechanics I can't find the ...
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The quantum state of the Universe

As far as I know, the two popular attempts to quantize gravity (string theory and loop quantum gravity) rely on unmodified quantum mechanics. Since they aim to become ToEs, this also mean that the ...
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Quantum to String: making the transition

We have a Hamiltonian containing a quantum simple harmonic oscillator coupled to a meter and a force. There is a term in the Hamiltonian that involves the oscillator position and the force, a term ...
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An ideal condition in Heisenbergs uncertainity principle

We all know that the Heisenberg uncertainity principle implies $\Delta x\, \Delta p\geq\frac{\hbar}{2}.$ But is there an ideal condition where we can measure $\Delta x$ to a particular precision and ...
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66 views

How do you isolate a single photon?

How do scientists/researchers isolate a single photon (for single photon sources)? How do they know they have isolated it? Is it really totally "isolated"? What is the photon isolated in? Sorry if ...
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36 views

Question about Hartle and Hawking's universal wavefunction?

My apologies in advance if this question is poorly worded or doesn't make any sense, however I have just finished reading into this theory and it seems as though Hawkings No Boundary Universe is ...
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Sums of operators in practice

Consider a one dimensional harmonic oscillator. We have: $$\hat{n} = \hat{a}^{\dagger} \hat{a} = \frac{m \omega}{2 \hbar} \hat{x}^2 + \frac{1}{2 \hbar m \omega} \hat{p}^2 - \frac{1}{2}$$ And: ...
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Motivating the ansatz for the infinitesimal translation operator

I'm reading Sakurai's Modern QM right now and in the first chapter he states a number of conditions required for a translation operator: unitarity, ...
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Atomic Brownian Motion

Since atoms 'wiggle' proportionally to their energy level, I have two questions: Does it last 'forever'? Absolute Zero question And so, is this 'flux' a fundamental force? Then as an extra ...
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Theoretically, is there anything in physics that prevents something like a transparent ipad or smartphone? [closed]

Also, is it possible to have electronic displays on the walls of a home? Is there anything in physics that prevents that? I guess I'm trying to ask if something like this is possible: ...
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Can entanglements themselves be entangled?

In other words, could there be higher dimensional entanglements between entanglements? For instance, this could allow us to entangle two entangled-far-away pairs to create a system of four entangled ...
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Dirac's remark that inspired Feynman when formulating path integral

When Feynman was trying to formulate path integral of quantum mechanics, he was inspired by Dirac's remark which roughly states that $e^{i\frac{S}{\hbar}}$corresponds to the transition amplitude, ...
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Why is uncertainty $\geq {\hbar}/{2} $ [duplicate]

Almost all uncertainties (for example the position-momentum uncertainty or time-energy uncertainty) are greater than ${\hbar}/{2} $. But what is the derivation of this uncertainty by Heisenberg? Is ...
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Physical interpretation of Probability Current vanishing inside Potential Barrier

In a Tunneling problem, if the $E_o<V$, we can show that the scattering wavefunction inside a rectangular barrier is a decaying exponential. The solution being real implies that the probability ...
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Difference between Hamiltonian in classical Mechanics and in quantum Mechanics

I have a question about difference between Hamiltonian function (the description of system in classical physics) and the Hamiltonian operator (quantum mechanics). I think that there two different ...