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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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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64 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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57 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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59 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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47 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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68 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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37 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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44 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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59 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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25 views

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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47 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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120 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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52 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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14 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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69 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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2answers
74 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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17 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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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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51 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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108 views

Are different interpretations of quantum mechanics empirically distinguishable?

Are the different interpretations of Quantum mechanics just different viewpoints of same physical reality? or the experiments can distinguish them? i mean are they empirically distinguishable or not? ...
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21 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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72 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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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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85 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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78 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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102 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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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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436 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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63 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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134 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 ...
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60 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 ...
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67 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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71 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.
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76 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 ...
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48 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\;=\; ...
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53 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 ...
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70 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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265 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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103 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 ...
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1answer
57 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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Bound states in 1D & 2D

Why does Mother Nature allow bound states in arbitrarily weak attractive potential in 2D but not in 3D? See, for example, this article: ...
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140 views

Dimension of separable state

I'm from a pure mathematics background (BSc and MSc). I’m reading Quantum Computing: From Linear Algebra to Physical Realization by Nakahara. Please can you help me to understand how the dimension ...
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53 views

What does “coherent wave function of a macroscopic body” mean?

What is meant by the "coherent wave function of a macroscopic body"? I found this phrase in a paper on QM, but am unfamiliar with the terminology.
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145 views

Inner products with orthonormal bases

Probably a stupid question here - I think it's a case of me not having sufficient mathematical background to follow this through. In Leonard Susskind's Theoretical Minimum book, he represents the ...
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52 views

Can we make a camera that fits in one of the bands of the double slit experiment?

So, in Young's double slit experiment, we see where the particle lands on the back wall. What if we were standing at the back wall, looking toward the slits? Could we gain more information not by ...
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Lack of scale in Schrödinger equation for square-inverse potential

I see that if we set our potential in schrodinger equation to be a inverse-square dependence we don't have a typical unit of length as we have for hydrogen atom. $$-{\hbar^2\over 2m}\nabla^2\psi + ...
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83 views

Quantum field theory: field operators in terms of creation/annihilation operators

I am learning Quantum Field Theory and there is a step in my notes that I do not really understand. It starts with the classical definitions of position $q$ and momentum $p$: $$ q = ...
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82 views

$\exp(i\alpha\hat {\bf n}\cdot{\bf \sigma} )=\cos\alpha I+i(\hat {\bf n}\cdot{\bf \sigma})\sin\alpha$

Could anyone tell me $\hat {\bf n}\cdot{\bf \sigma}$ is defined in such way? In the book they have not defined what is $n_z,n_x,n_y$. It is from Quantum Computing: From Linear Algebra to Physical ...
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Notation in a paper on quantum mechanics and gravitation (2)

I am currently reading the paper "Gravitation and quantum mechanics for macroscopic objects" by F. Karolyhazy (1966). The author defines formally rigorous equations in order to describe the decay of ...
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What does the notation $\Psi_k/(\Psi_k,\Psi_k)^{1/2} $ mean?

I am currently reading the paper "Gravitation and quantum mechanics for macroscopic objects" by F. Karolyhazy (1966). In his paper, he uses certain notation that I haven't come across before (he also ...