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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14answers
2k views

Why quantum mechanics?

Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
6
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1answer
236 views

Quantum Entanglement Versus Inflation in the Early Universe?

Quantum entanglement is one of the most fascinating and mysterious phenomena in nature. It needs no interactions, or any sort of exchange for it to take place. It is possible, not against any rules of ...
7
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4answers
651 views

How can one derive Schrödinger equation?

The Schrödinger equation is the basis to understanding quantum mechanics, but how can one derive it? I asked my instructor but he told me that it came from the experience of Schrödinger and his ...
0
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0answers
15 views

Correlation between Bohr-model and quantum physics

If you're looking at the probability of finding the electron of a hydrogen atom at a distance $r$ from the nucleus, it turns out that the Bohr model for the radius of the orbit only correlates with ...
3
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2answers
2k views

What is an energy eigenstate exactly?

Say you have energy eigenstates \begin{align} \begin{split} |+\rangle= \frac{1}{\sqrt{2}}|1{\rangle}+\frac{1}{\sqrt{2}}|2 \rangle \end{split} \end{align} \begin{align} \begin{split} |-\rangle= ...
21
votes
3answers
919 views

Hilbert space of harmonic oscillator: Countable vs uncountable?

Hm, this just occurred to me while answering another question: If I write the Hamiltonian for a harmonic oscillator as $$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$ then wouldn't one set of ...
5
votes
1answer
378 views

Hilbert space of a free particle: Countable or Uncountable?

This is obviously a follow on question to the Phys.SE post Hilbert space of harmonic oscillator: Countable vs uncountable? So I thought that the Hilbert space of a bound electron is countable, but ...
0
votes
0answers
68 views

Momentum operator in Dirac formalism

Could you derive the momentum operator as follows: Since $\mathcal{T}(\Delta x)=\exp(-ip_{x} \Delta x/ \hslash)$, if we set $\Delta x=x-0$ then it follows that $\left \langle x\right | ...
7
votes
1answer
139 views

Is there a formalism for talking about diagonality/commutativity of operators with respect to an overcomplete basis?

Consider a density matrix of a free particle in non-relativistic quantum mechanics. Nice, quasi-classical particles will be well-approximated by a wavepacket or a mixture of wavepackets. The ...
3
votes
2answers
180 views

1D Infinite Square Box Discrete Energy levels but Continous Momenta?

In the 1d particle in the box the energy of the particle should be completely determined by the momentum of the particle that you observe correct? So how can you have discrete energy levels and a ...
-2
votes
0answers
54 views

A new interpretation of QM [on hold]

Do you think that this new interpretation of quantum mechanics has solved the measurement problem completely as it claims? http://article.sapub.org/10.5923.j.ijtmp.20140405.04.html
4
votes
2answers
155 views

Is there any physical quantity that does not have uncertainty?

I saw this video and I got a thought: Is there any physical quantity that does not have uncertainty? Basic models are: for lenght for time end energy (so for mass too) and I realized that ...
0
votes
1answer
44 views

Finding the spectrum of a curious hamiltonian

I wish to analyse the following hamiltonian, i.e. find its eigenvalues and eigenstates. $$H = \frac{1}{2}\epsilon(\sigma _z \otimes \mathbb{1} + 1\otimes \sigma _z) - \Delta (\sigma _x \otimes \sigma ...
0
votes
0answers
25 views

Interpretation of angular momentum in semi-classical vector model

My Professor said that when we calculate the total angular momentum of multiparticles, in this case i.e. 2 particles, we can add total angular momentum by thinking this way, if both spins allign they ...
17
votes
11answers
2k views

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 ...
5
votes
2answers
73 views

Hydrogen energy levels and energy-time uncertainty principle

Some hydrogen atom exists in some excited quantum state, and after some time $\Delta t$ it's de-excited, emitting a photon carrying the energy difference. It is claimed that this photon will carry ...
6
votes
2answers
574 views

How is antimatter made?

How is antimatter made in laboratory? Can anyone explain, at the particle level, specifically how anti-protons and anti-electrons are made?
0
votes
1answer
29 views

Example of a state which is positive but its partial transpose is not positive

Could any one give me an example of a state whose density matrix is positive semidefinnite but partial transpose is not positive semidefinnite?
0
votes
1answer
79 views

Is there any defect in Rutherford's atomic model according to quantum theory?

According to quantum mechanics charged bodies do not emit energy. Then why the atomic model of Rutherford has the defects of collapsing nucleus, continues spectrum.
3
votes
1answer
64 views

Where does the partial derivative come from in Sakurai's derivation of the momentum operator?

How is the momentum operator derived in Dirac formalism? I am reading Quantum Mechanics by Sakurai and he gives the following derivation. But I don't understand how he goes from the third equation to ...
2
votes
2answers
101 views

Why do electrons orbit protons? [duplicate]

I was wondering why electrons orbited protons rather than protons orbiting electrons. My first thought was that it was due to the small amount of gravitational attraction between them that would ...
0
votes
1answer
43 views

Diffraction to be explained without Huygens principle

Can we explain diffraction without using Huygens principle?
0
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0answers
39 views

Bell's inequality

For a project, I'm planning to study Bell's inequality, which as far as I can gather is taken to rule out hidden variable theories of QM. I'm looking for recommendations of decent sources which derive ...
1
vote
4answers
95 views

Virtual particles/quantum tunneling - conservation of energy?

I'm confused as to how the above phenomena can take place since arent they breaking the law of conservation of energy (even, if temporarily)?
0
votes
1answer
28 views

Potential energy given to an electron in a time-varying electric field

Given a general electric field $\epsilon(t) $ directed in the z direction, how would we calculate the potential energy given to an electron as a result of this field?
2
votes
1answer
83 views

Solution of dynamics of density matrix

Given the dynamics of the density matrix: $ \frac{d}{d t}\begin{pmatrix} \rho_{00} & \rho_{01} \\ \rho_{10} & \rho_{11} \end{pmatrix} = \begin{pmatrix} \lambda ...
1
vote
1answer
166 views

Energy difference between symmetric and antisymmetric wavefunctions

Is there any energy difference between a particle in a symmetric wavefunction and an identical particle in an identical potential but in a state with an anti-symmetric wavefunction? Or is it ...
0
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0answers
59 views

About the meaning of quantum numbers [on hold]

could someone elaborate the idea of quantum numbers: Azimuthal quantum number (ℓ) Magnetic quantum number (m) Spin quantum number (s) I want to know: their physical meaning and the origin of ...
0
votes
0answers
10 views

Wavefunction of isomers

In quantum chemistry, the wavefunction for a molecule can be viewed as the output of a function $\xi(m, n_1,..., n_k)$ with $m, n_i \in \mathbb{Z}^+$ that returns a $|\psi\rangle$ that satisfies a ...
0
votes
0answers
51 views

Probability of spontaneous combustion [on hold]

Given the random background quantum noise, what is the probability that it will happen to concentrate in a particular location with sufficient quantity to cause a human being to spontaneously combust? ...
2
votes
1answer
70 views

Dirac Notation Question Appearing In a Projection

So I have a part of the energy eigenvalue equation that look like this: $$ \delta(\hat{x})|n\rangle $$ Where n is the energy basis of the Hamiltonian I'm considering. To deal with this, I tried ...
2
votes
3answers
177 views

How to derive $[x_i, F(\vec p)] = i \hbar \frac {\partial F(\vec p)}{\partial p_i}$

Wikipedia indicates that the following relation is "easily shown": $[x_i, F(\vec p)] = i \hbar \frac {\partial F(\vec p)}{\partial p_i}$, however I'm having some trouble showing it. I think I'm just ...
-4
votes
0answers
71 views

Possible theory of everything? [on hold]

Tell me if there is anything that sounds immediately incorrect about this possibility or if it's already been considered. We know that the universe can be in infinite different quantum states, but we ...
5
votes
1answer
91 views

Young Tableaux for $SU(3)$ representations vs. $j=1$ objects

I'm working through Sakurai's Modern Quantum Mechanics and in the section on Permutation Symmetry and Young Tableaux, he mentions that a tableau constructed of $\square = ...
7
votes
1answer
166 views

Why is there $1/2\pi$ in $\int\frac{dp}{2\pi}|p\rangle\langle p|$?

I'm reading Richard MacKenzie's lectures on path integrals and on page 7 he derives the propagator for the free particle as follows: $$ \begin{align} K &= \langle q'|e^{-iHT}|q\rangle \\ &= ...
0
votes
1answer
88 views

Are only 2 bits of information transmitted in quantum teleportation?

Prompted by the recent success in Delft, I've been reading a number of papers and articles about quantum teleportation. I'm comfortable with my understanding of most aspects but haven't found much ...
0
votes
0answers
35 views

Is this essay topic relating to my level of quantum physics? [on hold]

I am studying mathematics with a minor in physics. My mathematical skills therefore exceed my physics skills, and I have no much trouble with more advanced mathematical techniques. In our current ...
1
vote
1answer
33 views

Defining creation and annihilation operators

Creation and annihilation operators can be defined in several different ways, some more general than others. We usually choose to denote by $a$ the annihilation operator and by $a^\dagger$ the ...
2
votes
1answer
78 views

Linear vs. quadratic dispersion relation

In wave mechanics the dispersion relation between frequency $\omega$ and wave number $k$ is linear: $$\omega_n=c k_n$$ But in quantum mechanics, based on Schrödinger's equation, one can show that we ...
4
votes
3answers
191 views

Why particle number operator $\hat{N}$ is $\hat{a}^\dagger\hat{a}$ rather than $\hat{a}\hat{a}^\dagger$?

Both $\hat{a}^\dagger\hat{a}$ and $\hat{a}\hat{a}^\dagger$ are Hermitian, how do we know which one represents the particle number?
1
vote
2answers
94 views

How to understand “always create before we annihilate, not the other way around”?

On the book QFT in a Nutshell by A.Zee page 61 writes Always create before we annihilate, not the other way around. —Anonymous But in this Phys.SE question we are doing it the other way ...
1
vote
0answers
48 views

Chaotic behaviour re-obtained in QM

In classical mechanics, when we talk about chaotic systems (e.g. double pendulum), we always associate (or justify) them with the non-linearity(and non-integrability) of the differential equations ...
2
votes
1answer
94 views

Electron distribution around atom when moving

I do not have much experience on this but if an atom has some electrons around nucleus and the atom itself it is moving at some speed does that affect the distribution of electrons around? I am ...
6
votes
2answers
129 views

Semiclassical limit of Quantum Mechanics

I find myself often puzzled with the different definitions one gives to "semiclassical limits" in the context of quantum mechanics, in other words limits that eventually turn quantum mechanics into ...
1
vote
0answers
40 views

Time evolution operator of a periodic Hamiltonian

Suppose we have a Hamiltonian $H(t)$ with periodicity $T$. The time evolution operator in a full period is $$U_1=\cal{T}e^{-i\int_0^T H(t)\mathrm{d}t}$$, where $\cal{T}$ is time ordering operator; ...
14
votes
6answers
2k views

What is $\Delta t$ in the time-energy uncertainty principle?

In non-relativistic QM, the $\Delta E$ in the time-energy uncertainty principle is the limiting standard deviation of the set of energy measurements of $n$ identically prepared systems as $n$ goes to ...
1
vote
1answer
70 views

Wigner Threshold law in Photodetachment and Photoionization

I am writing this question here because I have a problem in understanding the Wigner Threshold law in Photodetachment and Photoionization. The Wigner Threshold Law is given by: $\sigma$=$E^{L+1/2}$. ...
3
votes
1answer
103 views

Can quantum mechanics be formulated without any reference to pictures?

NOTE: in the following with the word "picture" I refer to Schroedinger, Heisenberg, Interaction pictures, i.e. to the way the time-evolution is "distributed" between states and operators. We often ...
76
votes
5answers
23k views

What is the actual significance of the amplituhedron?

The news that physicists have discovered a geometrical object that simplifies a lot our models of quantum physics has recently became viral. For an outsider like me, it is difficult to actually ...
2
votes
0answers
22 views

Detailed Balance for Quantum Master Equations from System Hamiltonians with Degenerate Spectrum

Kossakowski, Andrzej, et al. ("Quantum detailed balance and KMS condition." Communications in Mathematical Physics 57.2 (1977): 97-110) gave a proof that the stationary state of a quantum dynamical ...