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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59 views

Can the simulation argument be ruled out? [closed]

I am neither a physicist nor a mathematician - simply an interested beholder of the current situation interested in quantum physics and quantum mechanics. So please bear with me regarding any ...
2
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1answer
75 views

Normalization of a wavefunction that's superposition of two unknown energy eigenfunctions

Question:$$\psi(x)=A(3u_1(x)+4u_2(x))$$where $u_1(x)$ and $u_2(x)$ are energy eigenfunctions. How to normalize function $\psi(x)$? My intuitive solution: I got ...
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1answer
30 views

Introductory Quantum, trouble with this boundary condition and potential

Working on problem 2.40 from Griffiths but can't seem to understand the first boundary condition. We are given the potential $V(x) = \left\{\begin{matrix} \infty & x < 0\\ ...
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2answers
41 views

Complexity of a physical system

Are there any accepted definitions quantifying the complexity of: a) macroscopic, classical mechanical systems (e.g., a bicycle) b) microscopic systems (ensembles of atoms)? By the way, I'm not ...
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0answers
34 views

Change of Basis For Pauli Matrix From Z Diagonal to X Diagonal Basis

I want to find a matrix such that it takes a spin z ket in the z basis, $$ \lvert S_z + \rangle_z $$ and operates on it, giving me a spin z ket in the x basis, $$ U \lvert S_z + \rangle_z = ...
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2answers
136 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 ...
4
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2answers
95 views

Motivating Complexification of Lie Algebras?

What is the motivation for complexifying a Lie algebra? In quantum mechanical angular momentum the commutation relations $$[J_x,J_y]=iJ_z, \quad [J_y,J_z] = iJ_x,\quad [J_z,J_x] = iJ_y$$ become, on ...
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12 views

Motivating Complexification of Lie Algebras? [duplicate]

What is the motivation for complexifying a Lie algebra? In quantum mechanical angular momentum the commutation relations $$[J_x,J_y]=iJ_z, [J_y,J_z] = iJ_x, [J_z,J_x] = iJ_y$$ become, on ...
2
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1answer
38 views

A vector function of a vector $\mathbf{S}$ must be given by a multiple of $\mathbf{S}$?

I've been reading Ballentine's Quantum Mechanics, A Modern Development and a statement made in Chapter 3 has been puzzling for me. In Chapter 3 of his book, Ballentine derives the kinematics and ...
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0answers
67 views

Schroedinger wave equation [closed]

Has there been any work on how the Schroedinger wave equation is affected in the stretched spacetime of a strong gravitational field in General relativity?. Rather than being a 'broad' question this ...
1
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1answer
69 views

Rewriting the Hydrogen Schrodinger Equation as a system of differential equations

I have only ever seen the Schrodinger equation for the hydrogen atom written out in a form like this: $$ -\frac{\hbar^2}{2\mu}\left[\frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2\frac{\partial ...
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1answer
37 views

Scattering and bound States

So from my understanding, as long as $E>0$ you will have scattering states and these scattering states will always result in an imaginary $\psi$, but bound states can also have an imaginary ...
0
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0answers
74 views

How to prove $\hat{p}|x\rangle=i\hbar\frac{\partial}{\partial x}|x\rangle$,using $[\hat{x},\hat{p}]=i\hbar$? [duplicate]

How to prove $$\hat{p}|x\rangle=i\hbar\frac{\partial}{\partial x}|x\rangle,$$ using $$[\hat{x},\hat{p}]=i\hbar~?$$ The question seems to be uncomplete because for any $f(x)$ ...
1
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2answers
65 views

Eigenvalues being physical observables

I think I'm comfortable with the PDE solutions to the Schrodinger equation. But as soon as we start putting these values in a matrix (in dirac notation), I lose my understanding and everything ...
2
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3answers
186 views

Is there an objective, external reality according to quantum physics?

In quantum physics, a particle can be in a superposition of two states until it is measured. In other words, the aforementioned particle doesn't have a definite state until it is "looked at" ...
2
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2answers
37 views

About completeness relation from discrete to continuous limit

In quantum mechanics, the completeness relation for discrete and continuous basis are $$\begin{align} \sum_n \lvert n \rangle \langle n\rvert &= 1 \tag{1} \\ \int \lvert x \rangle \langle x ...
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2answers
35 views

Determining bound states for delta function potential

I'm working on a problem out of Griffith's Intro to QM 2nd Ed. and it's asking to find the bound states for for the potential $V(x)=-\alpha[\delta(x+a)+\delta(x-a)]$ This is what I'm doing so far: ...
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0answers
27 views

Could we imagine spin as rotating probability densities (orbitals) in a kind of expanded orbital model?

I know there is no spin in orbital model. And it is always said there is no visualization for the spin. But why not just let the oribtals rotate with 4D quaternions in some 3D dynamic model?
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0answers
38 views

Quantam Computing Understading [closed]

I understand that quantam computing is in its infancy, but to help me understand it in laymen's term, the idea of having superposition & entanglement, is that not just having binary computing but ...
3
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4answers
103 views

Is this an entangled state?

Is the following state entangled? $\left| \psi \right> = \alpha_0 \beta_0 \left| 00 \right> + \alpha_0 \beta_1 \left| 01 \right> + 0 \left| 10 \right>+ \alpha_1 \beta_1 \left| 11 ...
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0answers
51 views

Free will theorem advice [duplicate]

I'm trying to understand the free will theorem which has been constructed by John Conway. Are they saying that particles have free will because they cause their behaviour in response to the ...
1
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1answer
43 views

Total magnetic moment in an atom

I have a doubt regarding the calculation of total angular momentum of electron in an atom.Which is the right way to do it? Method 1: Total magnetic moment $$ \begin{align} \vec{\mu_J} &= ...
3
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2answers
155 views

Is $0 | \psi \rangle=0$?

For example, the spin operator for spin 1 particle is $\hat{S}_z\doteq\hbar\begin{pmatrix} 1&&\\&0&\\&&-1\end{pmatrix}$ for state ...
0
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1answer
53 views

Why can't de Broglie waves be electromagnetic in nature?

We know that the wavelength of de Broglie waves for a photon is same as that of the wavelength of the electromagnetic radiation that carries this photon. Doesn't this prove that matter waves are em ...
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2answers
116 views

The Delta-Function Potential

I'm reading through Griffiths Intro to QM 2nd Ed. and when it comes to bound/scattering states (2.5) they say: $E<0 \implies$ bound state $E>0 \implies$ scattering state Why doesn't this ...
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2answers
68 views

Should the eigenkets be weighted in $|P\rangle = \sum\limits_{r}|\xi^r\rangle$?

Page 37 of Dirac's book The Principles of Quantum Mechanics, states The condition for the eigenstates of $\xi$ to form a complete set must thus be formulated, that any ket $|P\rangle$ can be ...
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2answers
67 views

Difficulty evaluating a complex integral on Griffiths

This actually a question from Griffiths QM. (Q2.21) I have difficulty understanding integrals involving imaginary components. In this example, it looks like the first term (encircled in red) explodes ...
2
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1answer
69 views

Ground state of BCS mean field Hamiltonian

I have question following the logics of BCS Theory regarding the ground state. First let me recap the logics of textbooks, for example, by Carsten Timm . After obtaining the interacting BCS ...
3
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1answer
79 views

What is the difference between correlation and entanglement?

I have read that not all correlated states are entangled. What is the difference between the two? Mathematically, it was stated that a system which can be put in the form of ...
1
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0answers
54 views

Hamiltonian for Electron in Magnetic Field with Symmetric Gauge in Polar Coordinates

I am new on the board and have a question about how to write the Hamiltonian for an electron in a magnetic field rotating at a fixed radius. I would like to write the hamiltonian using the symmetric ...
-6
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0answers
36 views

Seeking help to solve Q.3, Q.4 and Q.6 from the picture attached [closed]

Seeking help to solve Q.3, Q.4 and Q.6 from the picture attached.
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0answers
43 views

Find the eigenvalues and the unitary transformation that diagonalizes the Hamiltonian. Express the eigenstates in terms of old base states [closed]

Write the two-state Hamiltonian matrix in a certain basis |1>, |2> in a general form as H11 H12 H21 H22 Impose hermiticity of H. Find the eigenvalues and the unitary transformation that ...
0
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1answer
127 views

Can Bell's inequality violation be explained by the will of the scientist somehow affecting the experiment?

As far as I know, there are three possible ways to explain violation of Bell's inequality: violation of realism, violation of locality and violation of freedom. The first two are pretty ...
3
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2answers
355 views

What is meant by the spin of a particle? [duplicate]

I have been studying that electrons have quantum number called spin quantum number(s), this number can have either +1/2 or -1/2 value. If s=+1/2, the spin is clockwise and if s=-1/2, the spin is anti ...
2
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2answers
83 views

What does $g^{(2)}$ signify in quantum optics? And how to calculate it?

I have been studying research papers on Quantum Optics and non-linear optics. I frequently come across the $g^{(2)}$ value. What does it signify? What is its importance? How to calculate it? And ...
1
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1answer
45 views

Have $2s_{1/2}$ and $2p_{1/2}$ the same energy?

I have always known that p-states are more energetic than s-states. But in this picture I see the following: And it confused me. Could anyone explain if both levels have the same energy?
2
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2answers
73 views

Domain of simple quantum harmonic oscillator

When discussing the spectral theory of unbounded operators, one often starts with an operator defined on a densely defined subspace of your Hilbert space, and then proves that the operator is ...
1
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0answers
59 views

Use a Delayed Choice Quantum Eraser to communicate Faster Than Light [duplicate]

In the experiment setup picture of the Delayed choice quantum eraser, photons reach D0 and shows a pattern, before its quantum entangled counterparts reach one of D1, D2, D3, or D4. The pattern ...
7
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1answer
67 views

What causes Paulis Exclusion Principle?

Currently I'm taking an astrophysics class and has now come across electron degeneracy. As far as I understand, the reason why white dwarfs and such, does not collapse, is due to this, meaning that ...
0
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0answers
41 views

The electron: why can't it have both momentum and position [duplicate]

Total amateur here. I've been watching video lectures on Quantum Mechanics and it's said that there is no way to know both position and momentum of an electron at the same time. But is it because when ...
4
votes
1answer
136 views

Why is Planck's constant the same for all particles?

This question came to me while reading "Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from?". This question has a nice answer that explains that wave number has be ...
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0answers
18 views

Can anyone give me a simple proof for the sign change of electronic wavefunction when taken around a loop containing a conical intersection?

How and why does the sign of the electronic wavefunction changes when it is taken around a contour? For example, suppose the initial wavefunction is $f(s;S_0)$ at nuclear configuration $S_0$ and now ...
4
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2answers
72 views

Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from?

I'm curious where the expression $p=\frac{h}{\lambda}$ comes from. I know that for light, the following is true: $E=pc$ and $E=hf$ so, $pc=hf \Rightarrow p=\frac{hf}{c}=\frac{h}{\lambda}$ But how ...
0
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1answer
43 views

How to understand the unitary? [closed]

In the page 219 of Mahan's Many Particle Physics(3ed), there exists a transform $$ S=c^{\dagger}c\sum_q\frac{M_q}{\omega_q}(a_q^{\dagger}-a_q)$$ In order to prove that the transformation relating to ...
4
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3answers
193 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?
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0answers
13 views

Split property for type III algebras entails practical separability

I am reading Halvorson's thesis (http://philsci-archive.pitt.edu/346/1/main-new.pdf), however I don't understand a proof at p.50 where he tries to explain why the split property allows a local agent ...
4
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1answer
67 views

Where is quantum physics with regards to the periodic table?

In his Lecture's on Physics (circa 1960's) Richard Feynman wrote that so far physics has only been able to model (solve) the hydrogen and helium atoms. So now, more than 50 year's later where are we ...
0
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1answer
39 views

Question about one of the problems of the Bohr model

This is probably extremely basic physics that I don't know, but I'm still going to ask: Say in hydrogen, according to the Bohr model the electron is "really" orbiting the proton, and as a consequence ...
0
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1answer
138 views

Can an electron stand in place of proton like a ghost standing in place of you?

The atomic orbital refers to the physical region where the electron can be calculated to be present, as defined by the particular mathematical form of the orbital 1. The picture below shows the $1s$ ...
0
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2answers
54 views

Does quantum mechanics contradict macroscopic determinism?

I am wondering whether it is true to ask whether determinism is still completely viable at macroscopic scales given that the constituent particles behave according to QM when the dimensions get small ...