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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73 views

Can I state that $\Psi (x_1, \dots , x_n,t)= \sum_{i=1}^n a_i \psi (x_i,t) $ via superposition?

Given that the hamiltonian $\hat H$ of a system is a linear operator and $\dot \psi (x_i,t)$ does not depend on spatial coordinates $x_1, ..., x_n$ with bases $\hat e_1, ... , \hat e_n$ can I state ...
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1answer
319 views

Coercivity of a ferromagnetic material?

I understand that coercivity is the field/force required to demagnetize/magnetize a ferromagnetic material. What if we had two opposite magnetic fields of different strengths values H acting on the ...
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1answer
22 views

Probability density function of a particle for computation [on hold]

I'm writing a program, part of which relies on a particle being able to change location similar to a how a real particle would behave (pardon my physics). For example, on a grid of 100x100, a ...
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0answers
35 views

Quantum mechanical expectation of angular momentum along different axes

This is a question from Concepts of Quantum Mechanics by Mathur & Singh, and I don't know where I should start from: Show that, for a state $|j,m \rangle$, corresponding to a definite value of ...
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1answer
17 views

Uncertainty of energy for harmonic oscillator at ground state and first excited state

How does one calculate the energy uncertainty of the harmonic oscillator in the ground state and first excited state?
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62 views

How does one normalize this wavefunction? [on hold]

Here is the question: So I could write $ N = \dfrac{1}{{\sqrt{<Ψ|Ψ>}}} $, right? Considering the parentheses in the exponential term, it looks like a good idea to switch to spherical polar ...
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1answer
24 views

Non-degenerate or degenerate perturbation theory for a non-degenerate level of a system with other levels degenerate?

To decide whether I have to use non-degenerate or degenerate perturbation theory, I have to look only on whether the energy level I am calculating corrections to is degenerate, the degree of ...
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2answers
164 views

Why are the zeroth order terms in degenerate perturbation theory the eigenstates of the perturbing Hamiltonian?

I have for quite some time now tried to find a satisfactory answer to this, but I haven't yet. In perturbation theory, with small parameter $\lambda$, we expand the eigenstate as $$| E \rangle=| ...
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1answer
60 views

Can I have superposition equation? [on hold]

I would like superposition equation. I learn functions, boundaries of strings, boundaries of functions, differential equations, derivatives and integrals to understand superpositions from Mathematical ...
2
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1answer
96 views

Eigenfunctions of Schrödinger equation

Why are solutions of the Schrödinger equation called eigenfunctions? For an electron moving in one dimensional lattice the eigenfunctions are given by$$\psi(x)=u_k(x)e^{ikx}.$
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5answers
691 views

Is the wave function objective or subjective?

Here is a question I am curious about. Is the wave function objective or subjective, or is such a question meaningless? Conventionally, subjectivity is as follows: if a quantity is subjective then ...
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0answers
55 views

How to check whether Schrödinger's cat was in superposition of states?

Suppose we can make an arbitrarily precise preparation of a Schrödinger's cat (and isolate it arbitrarily well so that decoherence is not a problem). If we prepare lots of cats in this state, what ...
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1answer
145 views

Poles for a particle scattered in a delta potential

I am working on problem a professor gave me to get an idea for the research he does, and have hit a point where I'm having a difficult time seeing where I need to go from where I'm at. I would also ...
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0answers
21 views

How to derive De Haas–van Alphen effect?

I was reading Solid State Physics by Kittel and they manage to derive De Haas–van Alphen effect by invoking the Bohr-Sommerfeld model. This feels unsatisfactory to me. Can someone derive this using ...
4
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1answer
144 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 ...
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4answers
172 views

Is nature quantized?

I was reading Planck's postulate the other day on Wikipedia and couldn't help but noticing the sentence: "...is the postulate that the energy of oscillators in a black body is quantized..." ...
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3answers
129 views

What are correlated magnetic moments?

My book has the following sentence and I don't understand what correlation or lack of correlation means: At high temperature the magnetic moments of adjacent atoms are uncorrelated (to maximize ...
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1answer
81 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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2answers
42 views

Eigenstate vs collapsed wave function

An eigenstate, or determinate state, is a state where the measurement of some observable always yields the same result. This means that the standard deviation of the observable is zero. If a ...
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2answers
148 views

Why does a magnetic field raise the ground state energy of an electrical particle?

I heard a statement that the ground state energy of a electrical particle in a magnetic field is larger than its ground state energy without the magnetic field. I just heard this statement. This ...
1
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1answer
80 views

Particles that are distinguishable and indistiguishable at the same time

Thinking about a question and my answer to it and another question I asked earlier. I've come up with the following problem: Consider two otherwise very similar marbles, a red one and a blue one. Let ...
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2answers
69 views

Understanding the interpretation of wave-particle duality by W.L.Bragg

W.L.Bragg, the pioneer in x-ray diffraction, gave this lucid but vivid interpretation:"The dividing line between the wave & particle nature of matter & radiation is the moment now. As this ...
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7answers
2k views

Does electron being many places at the same time violate Physics laws?

The following passage has been extracted from the book Parallel Worlds, by Michio Kaku: Because of uncertainty, the electron does not exist at any single point, but exists in all possible ...
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0answers
22 views

Is it possible to get the (Pauli) repulsive term in the Lennard-Jones potential from theoretical considerations?

Title says it: Is it possible to get the form of the (Pauli) repulsive term in the Lennard-Jones potential from theoretical considerations, or is it purely found experimentally through fits?
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1answer
68 views

Perturbations in arbitrary dimensions

In general is it acceptable to say that if a perturbation is in only one spatial direction then the energy eigenvalue to second order is only changed in that spatial direction? For example 3D ...
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0answers
23 views

Continuum Wave Function for the electron

I'm trying to understand certain processes like the photoelectric effect and Bremsstrahlung. In Bremsstrahlung I need to use the wave function of an electron coming from the continuum, and there is ...
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0answers
39 views

Quantum relativistic effects

I was performing a thought experiment: let us assume an object is traveling so close to the speed of light that the length of the object is small enough for quantum effects to become noticeable to a ...
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2answers
47 views

When generalizing from discrete (but infinite) eigenstates to continuous eigenstates, Why do we change the definition?

The propagator function for discrete eigenstates is $$u(t)=\sum_{n=1}^{\infty}|E_n\rangle\langle E_n|e^{-iE_nt/ \hbar } \tag{1}\ .$$ But when we have continuous eigenstates, (like for the case of ...
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1answer
243 views

Quantum mechanics, operator commutes with Hamiltonian

My textbook said, if an operator $\hat{O}$ commutes with the Hamiltonian, then we can use the eigen vectors of the Hamiltonian as a basis of the Hilbert space, then express the operator $\hat{O}$ in ...
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1answer
46 views

Question about angular momentum operator

To show that the eigenvalue to $L^2$ is proportional to $\hbar^2$ is shown from $L_z=xP_y-yP_x$ $p_y=-i\hbar\frac{\partial}{\partial y}$ $p_x=-i\hbar\frac{\partial}{\partial x}$ ...
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1answer
90 views

Size of hydrogenic atoms

Positronium consists of an electron and a positron. By what factor is a positronium atom bigger than a hydrogen atom? The solution has been explained to me. The characteristic length when solving ...
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1answer
38 views

What is the exhaustive set of experiments a quantum theory has to satisfy?

Any theory that is to explain the world correctly has to provide a mechanism by which the interesting results of quantum mechanics happen (e.g. diffraction patterns, momentum/position uncertainty, ...
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2answers
38 views

Books on Quantum Measurement

I have been trying to understand clearly the concept of non locality, hidden variables, quantum measurement etc through research papers. I also read Quantum Theory and measurment by Wheeler and Zurek ...
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1answer
791 views

What're the relations and differences between slave-fermion and slave-boson formalism?

As we know, in condensed matter theory, especially in dealing with strongly correlated systems, physicists have constructed various "peculiar" slave-fermion and slave-boson theories. For example, For ...
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1answer
210 views

Two-state Hamiltonian matrix in basis

I have a homework problem as following: Write the two-state Hamiltonian matrix in a certain basis |1>, |2> in a general form as \begin{array}{ccc} H_{11} & H_{12} \\ H_{21} & H_{22} ...
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4answers
74 views

Is energy of a quantum mechanical moving particle conserved?

From the Schroedinger equation $$ H\psi=E\psi, $$ if we want to measure the total energy of a quantum mechanical moving particle, then we have to apply the Hamiltonian operator to the wave function ...
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0answers
31 views

How does Sachs derive QM mass term from general relativity?

I am interested in finding Mendel Sachs' derivation of the mass term in the Dirac equation, using the covariant derivative terms. The discussions as to the merits of Dr. Sachs' work are often prefaced ...
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2answers
65 views

How to connect these two formulations regarding the need for a density matrix in quantum mechanics?

I found these two formulations: The density matrix is: 1) "needed if we consider a system that is part of a larger closed system." 2) "needed for a system to be ...
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2answers
107 views

Proving that conservation of momentum doesn't apply to electron in H-atom

To prove that the conservation of linear momentum doesn't apply to electron in H-atom, is it sufficient to show that angular momentum operator ($\hat L$) and momentum operator ($\hat p$) do not ...
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1answer
71 views

Superposition and simultaneous observation

Trying to understand superposition. Ok, so double slit experiment. The multiple paths the particle simultaneously travels interfere with each other but as it is absorbed, it chooses one "actual" ...
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3answers
131 views

How does independence of two systems follows from the fact that they are both completely described?

A quote from Landau & Lifshitz (Quantum Mechanics - Non-relativistic Theory, §2): "Let us consider a system composed of two parts, and suppose that the state of this system is given in such a way ...
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7answers
3k views

Does electron in wave form have mass?

I heard from my lecturer that electron has dual nature. For that instance in young's double slit experiment electron exhibits as a particle at ends but it acts as a wave in between the ends. It under ...
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0answers
41 views

Time evolution of a discrete 1-d lattice of spin-(1/2) particles under a given Hamiltonian, or special cases thereof

I am trying to get some feel for the dynamics induced on a discrete 1-d lattice of spin-(1/2) quantum particles by the following Hamiltonian $\hat{H} = \sum_{i, j} r_{i j} \left[ ...
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0answers
31 views

Functions of commuting operators and interactions

The action of a function of an operator $A$ can be determined by the action on the eigenstates of $A$. If I have two commuting operators $A$ and $B$ and $|a,b\rangle$ is a common eigenstate, I get ...
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1answer
40 views

Quantum mechanics for playmen [on hold]

I am a student who is working on a small game and I played around with the idea of using Quantum Mechanics as the base of the game. Which concepts and results would be cool to play around with ...
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0answers
27 views

Quantum Fields From Cluster-Decomposition Principle

My question is asking for an explanation of Weinberg's claim that QFT is the only way to satisfy Lorentz invariance and the cluster-decomposition principle. The theory is in his QFT Vol. 1. Below I've ...
2
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1answer
755 views

Can conservation of momentum be violated?

The law of the conservation of momentum was accepted for year-hundreds. Even in Quantum field theory every particle collision must be momentum-conserving if there is homogenity in space. Can this ...
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1answer
117 views

Does magnetic monopole violate $U(1)$ gauge symmetry?

Does a magnetic monopole violate $U(1)$ gauge symmetry? In what sense and why? Insofar as I know, there are at least two types of magnetic monopoles. One is the Dirac monopole while the other is the ...
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0answers
15 views

Commutation of Magnetic Translation Operator with Hamiltonian [on hold]

How can I prove that magneic translation operator commutes with Hamiltonian where the translation operator does not for a non-zero non uniform magnetic field in general?
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2answers
135 views

Spin Control and Entanglement

I have a thought-experiment sort of question and I don't know where to start. Suppose you have an entangled pair, e1 and e2, and you split them. Then BEFORE reading them, you spin control e1 to +, ...