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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95 views

Unitarity of PMNS matrix

Why should the neutrino mixing matrix (PMNS matrix) be unitary? Is the unitarity dictated by experiments or is it a theoretical demand?
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0answers
39 views

Why quantum theories are good? [duplicate]

Why quantum theories are good and why people are seeking the quantum version of physical theories like that quantum gravity?
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0answers
44 views

Zero Energy States in 2D Systems

Since we are on a planar system (2D system) the massless Dirac equation reads $$\vec{\alpha}\cdot(\vec{p}-e\vec{A})\psi_E=E\psi_E$$ Here Dirac matrices are Pauli matrices ($\alpha^1=-\sigma^2$ , ...
2
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0answers
72 views

Entanglement entropy and area law

I am currently reading a review "Area law for the entanglement entropy" by Eisert, Cramer and Plenio (2010). From what I understand: In one dimension, for local gapped models, we have an area law ...
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6answers
2k views

Why is superdeterminism generally regarded as a joke? [closed]

Before anything, I'm sorry for being an outsider coming to opine about your field. This is almost always a stupid decision, but I do have a good justification for this case. I've been reading about ...
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0answers
20 views

Suggestions about these books [duplicate]

Which are the best books for the following( introductory level)? quantum mechanics classical mechanics statistical physics particle physics
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2answers
81 views

Quantum Mechanics: Momentum operator questions [closed]

I'm asked to determine $\hat{P}|\Psi_0\rangle$, $\langle{\hat{P}}\rangle$, and $\langle\hat{P}^2\rangle$ for $$\Psi_0(u) = \psi_0 + 2\psi_1$$ I understand how to make the matrix for $P$ in regards ...
1
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1answer
62 views

Why does Matter occupies space? Matter and space are two things… If Space does not has mass, why should matter have space-ful nature?

This thought has completely changed my perspective towards matter. If the matter in a star can collapse to a point to form a Black hole, surely the true nature of matter should be able explain this ...
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6answers
2k views

If I drop a leaf twice from the height of a tree in a completely controlled environment, will the trajectory in each case be the same?

Putting my question in other words, can earth form again if a similar initial universe condition is given? The uncertainty principle says that we cannot tell with certainty the position of a particle ...
0
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0answers
24 views

Bragg's diffraction and Simon's problem

In Preskill's notes, John Preskill goes as If we scatter a photon off of a periodic array of needles , the photon is likely to be scattered in one of a set of preferred directions , where the ...
6
votes
2answers
390 views

Has the collapse of wave function due to observation been recorded?

I've seen pictures like this one, which depict the outcome of the Double-slit experiment with wave-like or particle features, depending how measurement has taken place. The graphic showing ...
2
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2answers
65 views

Conjugate of an operator applied to a function

In section 6.3.1 of the following MIT Open Course Ware (PDF) (22-02, Introduction to Applied Nuclear Engineering), the author, Prof Paola Cappellaro, derives Heisenberg's equation using the definition ...
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0answers
53 views

Why Green's function will diverge at the same spacetime point?

In $d+1$ dimensional quantum field theory, the 2-point Green's function will diverge at the same spacetime point when $d\geq1$. When $d=0$, $\phi(t)=q(t)$, that is the case of QM, and 2-point Green's ...
1
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1answer
36 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 ...
1
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2answers
45 views

Unitary transformation between complete + orthonormal bases

Suppose the complete orthonormal bases $\{|\psi_n\rangle\}$ and $\{|\psi{'}_n\rangle\}$ are related by the transformation matrix $U$: $$ |\psi{'}_n\rangle = U|\psi_n\rangle \\ \langle\psi{'}_n| = ...
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0answers
46 views

Four-current, Induced Charge and Magnetic Flux

I'm studying Jackiw's "Fractional Charge and Zero Modes for Planar Systems in a Magnetic Field" DOI: 10.1103/PhysRevD.33.2500 but I have difficulties at some points. One of the problems is $$\langle ...
1
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1answer
43 views

Pure State Non-zero Entropy Paradox

Entropy measures the number of microscopic states of a given system. For a pure state, the count is one. Thus, entropy ~ log(1) = zero. However, on the other hand, if we calculate the entropy of ...
0
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1answer
42 views

Can scientists tell the energy levels of the atom?

In the hydrogen spectral series how did the scientists know the number of the energy level which the electron is moving from or to?
4
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1answer
69 views

Orthogonality of summed wave functions

Problem. I know that the two wave functions $\Psi_1$ and $\Psi_2$ are all normalized and orthogonal. I now want to prove that this implies that $\Psi_3=\Psi_1+\Psi_2$ is orthogonal to ...
3
votes
3answers
116 views

Advantage of taking qutrits in place of qubits

In general, all the quantum algorithms which I have read so far use qubits (so the space is $\mathbb{C}^2$) and the tensor products of the qubit spaces (space is ${\mathbb{C}^2}^{\otimes n}$). So my ...
2
votes
2answers
105 views

Computer simulation of Schrödinger equation [duplicate]

I am looking for a computer program which simulates the Schrödinger equation (say for a single particle) in two dimensions and for potentials and initial states specified by the user. Typical ...
0
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1answer
43 views

Physically realizable quantum circuits

How do we decide whether a quantum circuit can be realized physically or not ? I was wondering for physical realization of Shor's factoring algorithm using NMR ( I mean can we do it? ).
5
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1answer
97 views

Is there a handwavy way to explain what quantum correlation means?

Is there a simple way to explain the difference between a classical and truly quantum correlation to a non-quantum person who has basic understanding classical correlation? I mean without invoking ...
4
votes
1answer
41 views

Effect of pressure increase on electron orbital wave functions

One of my nuclear physics exercises was to find out if increasing the pressure of a sample of $^{7}\textrm{Be}$ would increase the chance of electron capture to $^{7}\textrm{Li}$ occur. My reasoning ...
2
votes
1answer
52 views

A good book for Quantum Cryptography

I am interested in Quantum Information and Cryptography in particular. I have gone through Neilson's text and Preskill's notes . Can someone suggest me some good text for Quantum Cryptography ? I ...
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0answers
28 views

Positivity and Complete positivity of Simon Map [migrated]

Simon map in a specific basis is defined as $$ \left[ {\begin{array}{ccc} A & B & C \\ D & E & F \\ G & H & I \\ \end{array} } \right] \rightarrow \left[ ...
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2answers
77 views

State of constant motion

Why does an object remains in its state of constant motion if there are no forces acting on that object? My understanding is that all the energy of the motion will be kept inside and a change in the ...
1
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0answers
32 views

Is the reduction map completely positive? [duplicate]

I am struggling with proving the complete positivity of a general map ( granted it is CP ). The reduction map is defined as $$ \rho \rightarrow \mathrm{Tr}(\rho)I - \rho $$ It is a trivial job to ...
0
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1answer
61 views

Design a quantum circuit from a matrix

I have unitary matrix and I would find the quantum circuit associated. There are 3 qubits input so it's a 8x8 matrix but it's not a simple operation. The number of gates is not specified. Is there a ...
5
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3answers
447 views

How are anti-matter atoms created?

What is the reaction, or reactions that make anti-matter? I don't understand how anti-matter is created by CERN if interaction with normal matter causes annihilation.
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1answer
46 views
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0answers
36 views

Adiabatic approximation and time-dependent problems

I am an undergraduate physics student. I have a question in approximation methods for time-dependent problems in quantum mechanics. I read the proof of the adiabatic theorem but I didn't understand ...
1
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1answer
28 views

Quantum Key Distribution (QKD) Upper and Lower Bounds

Many papers on Quantum Key Distribution protocols discuss the protocols upper and lower bounds (on quantum bit error rate QBER). For example, BB84 has a lower bound of 11% and an upper bound of ...
1
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1answer
30 views

Uncertainty Definition QM

On my introductory course in Quantum Mechanics, the uncertainty of an operator $A$ in the state $\psi$ is defined by $$(\Delta A)^2_{\psi}=\langle(A-\langle A \rangle_{\psi})^2\rangle _{\psi}$$ I'm ...
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1answer
34 views

Expectation of dipole is vector in x direction

So I am asked to find a state $|\Psi(t)\rangle$ in terms of the hydrogen wave functions, such that the expectation of the dipole operator -$e\hat r$ is a vector in the x direction. I am not ...
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2answers
66 views

Quantum Expectation Values

I'm having trouble understanding the motivation for the definition of the expectation of a self adjoint operator $A$: $$\langle A \rangle _\psi=\int_{\mathbb{R}}\psi^*A\hspace{0.2cm} \psi ...
0
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3answers
59 views

Commutator summation notation

I have the relation $ e^L M e^{-L}=\sum_{n=0}^\infty \frac 1{n!} [L,M]_{(n)}$ where $L$ and $M$ are operators. What does the subscript $n$ after the commutator bracket denote?
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0answers
39 views

How to find density matrix?

The Beam-splitter matrix is $ B = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1\\ 1 & -1 \end{pmatrix} $. I want to apply $a^{\dagger}_{1}a^{\dagger}_{2} |00\rangle_{12}$ as the input state for ...
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0answers
25 views

Calculating the $J$ value for atomic terms, having a lot of trouble with this. Already attempted

I am trying to understand this, and want to be very very clear. This is a homework question but I already attempted to answer it, so please don't put this question on hold. The question What ...
22
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3answers
1k views

Why is an electron still an elementary particle after absorbing / emitting a photon?

When an electron absorbs a photon, does the photon become electron "stuff" (energy); or, is it contained within the electron as a discrete "something"?
2
votes
1answer
95 views

Differential equation for evolution of probability density in Quantum Mechanics?

I have come up with this differential equation for the evolution of $\vert \Psi \vert^2$, the probability density in quantum mechanics. Is there a name for this equation? Is the logic sound? So I ...
0
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0answers
32 views

How can we show that a map is a completely positive map? [migrated]

I am doing a homework problem where I have to find whether the map $$ \rho ~\rightarrow~ {\rm tr}(\rho) I - \rho $$ is completely positive. If the map is not completely positive, a counter-example ...
0
votes
3answers
64 views

Evaluating position vector between 2 hydrogen states

I am trying to find the quantity: $$\langle1,0,0|\vec r|2,0,0\rangle$$ Where $|n,l,m\rangle$ are the hydrogen states. For this, can I just integrate r from? 0 to infinity? Or do I have to break it ...
1
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1answer
167 views

Hilbert space in quantum mechanics

I think in quantum mechanics we assign to each system a specific Hilbert space i.e. if systems are different then their Hilbert spaces are different. Is this true? If not why? For differernt system I ...
0
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1answer
40 views

Quantum Mechanics - Rectangular Potential Barrier - Normalisation

I have a quick question regarding the normalisation of the wave function of a particle incident on a potential barrier specifically regarding the normalisation of the wave functions. The problem is ...
1
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1answer
48 views

Perturbation theory in quantum mechanics

In perturbation theory perturbed eigenstates expanded by unperturbed eigenstates, but we know when the system perturbed its Hilbert space altered and hence its basis changed, then we can't state this ...
0
votes
2answers
49 views

Which coordinate system confirms quantum-level experimental data?

We often use the Cartesian coordinate system, since it is the naive approach at macro level (placing a box just "next to" or "above" the other box). There are, however, many more such systems, incl. ...
1
vote
1answer
50 views

Stern Gerlach with spin in opposite directions

So for the Stern-Gerlach apparatus, we assume that we either have a particle spin up or spin down. We also have the varying field, $\partial B/\partial z$. This initial configuration results in the ...
2
votes
2answers
252 views

Determinism loophole?

I was thinking about the question I posted yesterday, and I thought of a better way to ask it. I'm trying to figure out why QM necessitates "pure randomness". Assume you have a photon that has a ...
0
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0answers
18 views

Angular Momentum Expectation in Magnetic Field

I am trying to find the time dependent expectation value for J ($\langle J(t) \rangle$) for a spin 3/2 particle in a uniform magnetic field (in the z direction). My method is as follows: ...