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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48 views

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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2answers
547 views

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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2answers
89 views

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 ...
3
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2answers
158 views

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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1answer
233 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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1answer
394 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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2answers
210 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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37 views

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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2answers
97 views

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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1answer
77 views

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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2answers
178 views

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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1answer
96 views

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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0answers
63 views

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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1answer
55 views

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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1answer
250 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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1answer
118 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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1answer
50 views

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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1answer
117 views

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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1answer
87 views

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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1answer
283 views

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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2answers
65 views

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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1answer
118 views

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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1answer
508 views

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 ...
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3answers
111 views

Are there two aspects of Born's rule?

I am having some problem understanding Born's rule. I am getting a little bit confused. Here it goes; Let $f(x,t)$ be a solution of Schrodinger equation. Then Born's rule says that the square modulus ...
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0answers
23 views

What is the temperature evolution of the conductance of a quantum chaotic system?

I read this really nice article by Abanin and Levitov: http://arxiv.org/pdf/0704.3608.pdf They argued that the mixing of the quantum edge channel at the vicinity of a PN junction is described by the ...
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0answers
34 views

Uncertain if invoking uncertainty principle for wave function is handwaving [duplicate]

Why doesn't the electron collapse onto the proton in a hydrogen atom? One explanation seems to be given by the Heisenberg uncertainty principle, which follows from the purely physical assertion that ...
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0answers
68 views

States of “positronium” with chiral fermions?

When I combine positron and electron to form positronium, or generically two spin 1/2 particles, I have four possible spin combinations that arrange into a singlet and a triplet state, which in turn ...
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458 views

Are different interpretations of quantum mechanics empirically distinguishable?

Are the different interpretations of Quantum mechanics just different viewpoints of the same physical reality? Or can experiments distinguish them? Are they empirically distinguishable or not? I have ...
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0answers
28 views

Problem books like I.E. Irodov for advanced physics [duplicate]

I really enjoyed doing problems from Irodov while learning introductory physics. But I am not able to find a book like that for Graduate level physics. Can you suggest me a book which has good (and ...
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1answer
100 views

How can I solve an equation involving partial trace?

I am unable to find the solution to the following equation: Tr$_{2}[U(|\psi\rangle \langle\psi|\otimes \rho)U^{\dagger}]=\rho$ Here $\psi$ is state vector representing a qubit and $\rho$ state of ...
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0answers
39 views

Using local U(1) Transformation to solve Problem in Path Integral [duplicate]

When we develop photon path integral, we assume that the current is always conserved. But if we consider interaction between electron/positron and photon, the Noether current is conserved only when ...
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1answer
116 views

Proof involving tensor product

I am trying to prove when the following holds: $$|a\rangle |b\rangle \langle c|\langle d| = |a\rangle \langle c| \otimes |b\rangle \langle d|$$ where $\otimes$ stands for tensor product and the ...
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2answers
107 views

Is negative mass for a bound system of two particles forbidden?

Is there any theorem that forbids the bound system of two massive particles to have negative mass?
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0answers
126 views

Eigenvalue of the adiabatic Hamiltonian of Farhi's three qubit 2-SAT problem

I was trying to reproduce example 3.3 of Quantum Computation by Adiabatic Evolution by Edward Farhi et. al. This is an adiabatic algorithm to solve an instance of three qubits 2-SAT problem. I think ...
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0answers
92 views

Problem with derivation of phonons in crystal

In this derivation of phonon solutions, everywhere, we are forcefully assuming the wavelike characteristics along the length of the chain. While all we can deduce for finding out the fundamental ...
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4answers
1k views

Intuitive meaning of the exponential form of an unitary operator in Quantum Mechanics

I'm an undergraduate student in Chemistry currently studying quantum mechanics and I have a problem with unitary transformations. Here in my book, it is stated that Every unitary operator ...
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1answer
113 views

Quartic terms as two particle interaction?

In some lecture notes I found the sentence: [...] considering two toy models: the classical and quantum harmonic oscillator with quartic perturbation. The quartic terms $\sim x^4$ and $\sim \hat x ...
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0answers
350 views

Propagators, path Integrals, transition amplitudes, Green's functions etc

I'm trying to make a simple conceptual map regarding some of the things in the title as they pertain to quantum mechanics and or quantum field theory, and I'm finding that I'm a little perplexed about ...
2
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3answers
114 views

Koopmann von Neumann (KvN) Theory

I was just wondering does anyone have any informative sources apart from the obvious wikipedia articles regarding Koopmann von Neumann (KvN) theory? Or if its possible could someone explain the basic ...
2
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1answer
202 views

Does the momentum operator commute with the Pauli matrix?

I tried to calculate the effect of spin orbit coupling $H_s=\alpha(\sigma_xp_y-\sigma_yp_x)$ as in the Rashba effect. But I just found out that it is not hermitian. Some paper propose some way by ...
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1answer
95 views

Is the spin and charge of an atom a quantum or classical concept?

I have no idea whether these properties of an atom fall under quantum or classical physics, or perhaps both. Some clarification would be helpful.
2
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1answer
80 views

Is there a chance an object isn't where we think it is?

At first, I know the question sounds ambiguous and maybe pseudo-scientific, but it's a thing I've been arguing about with my colleage for quite some time and while neither of us knows much about ...
2
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1answer
58 views

How does Dirac show that $\langle B|\bar{\bar{\alpha}}|P\rangle\;=\; \overline{\langle P|{\bar{\alpha}}|B\rangle}\;=\; \langle B|{\alpha}|P\rangle$?

Dirac shows that the conjugate imaginary of $\langle \!P|\alpha$ is $\bar{\alpha} |P\!\rangle$ and then starts with the identity on page 27 in his book: $$\langle B|\bar{{\alpha}}|P\rangle\;=\; ...
3
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0answers
62 views

How to check whether a given $W(x,p)$ represents a Wigner function of a physical state?

For simplicity let us consider one-dimensional quantum-mechanical systems only. Given any state $\rho\in\mathcal{B}(\mathcal{H})$ and its Wigner function $W_\rho(x,p)$, there are several properties it ...
2
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0answers
119 views

Question on spin-orbit interaction

When you study the spin-orbit interaction in quantum mechanics, even for a simple hydrogen atom, you find only the electric field in the nucleus reference system, while in the electron reference ...
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2answers
381 views

What is the spin of an electron along the x-axis?

I know that an electron or any other particle for that matter, has a measured spin which is either up or down. This spin is along the z-axis. But what if we do not measure it along the z-axis and do ...
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2answers
57 views

Why photon has a wave nature? [duplicate]

Wave theory does not account for the photon model, which was developed only to explain quantum effects like photoelectric effect. Then why do we talk about a photon's reflection and rarefaction, as ...
0
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4answers
158 views

Can an arrangement of particles be duplicated precisly?

Is it possible to teleport or clone someone or something? After watching this TED talk by Max Tegmark - https://www.youtube.com/watch?v=GzCvlFRISIM I find myself wondering if it is then possible to ...
2
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1answer
78 views

Rate of change of a normalised wave function

I'm reading Weinberg's Lectures on QM. On top of p23 it says $$i\hbar\frac{d}{dt}\int|\psi(x,t)|^2d^3x=i\hbar\int\psi^*(x,t)\frac{\partial}{\partial ...
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0answers
119 views

Bound states in 1D & 2D [duplicate]

Why does Mother Nature allow bound states in arbitrarily weak attractive potential in 2D but not in 3D? See, for example, this article, arXiv:math-ph/0208011.