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 quantum-field-...

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81 views

Where does the position operator come from?

In quantum mechanics the momentum and energy operators appear in Schroedinger's equation. In fact in the derivation of Schroedinger's equation from the classical wave equation the momentum operator ...
-1
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2answers
71 views

An unknow atom has the shown energy levels

In an excersice i found, a supposed atom called fictitious (Fi) has the following energy levels: Then i´m asked: A) The energies of the emitted photons after a gas of Fi is bombarded with ...
5
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2answers
103 views

String quantization and Malament's theorem

Malament's theorem posits that, given a few assumptions on relativistic QM, it is impossible to have localized particles. For $E_\Delta$ the proposition that a particle is certain to be found within a ...
3
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1answer
64 views

A Question on energy of electromagnetic wave

( I initially started to ask, "since according to Quantum-theory of light; the energy of a photon, depends only on the frequency of light-wave (E = h * nu), and no-mention of amplitude. So, does the ...
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0answers
55 views

Uncertainty principle explanation

Just finished reading "In Search of Schrödinger's Cat". I am currently trying to explain the Uncertainty principle to myself as if I was 5. Concretely, why it is not possible to measure both position ...
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1answer
50 views

Dimension of Hilbert space of spin $1/2$ identical particles?

Consider a system of $N$ spin $1/2$ particles. Assume the spin is the only degree of freedom and hence there is no spatial component. Then the dimension of the Hilbert space in this case is $2^N$. ...
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1answer
53 views

Why can't we use a capacitor to detect electrons in the electron double slit experiment?

So, basically I have been learning Quantum Mechanics online and I leant about the double slit experiment with electrons, wherein if you try to detect an electron with a light source having wavelength ...
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2answers
61 views

Energy Quantization

Why a free particle gives rise to Continuous Spectrum energy eigenvalues where particle in the Bound States provide the quantization?
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0answers
41 views

Locality and nonexistence of local hidden variables implies MWI?

The violation of Bell's inequality implies (under reasonable assumptions, let's not consider superdeterministic theories here) that there can be no local deterministic hidden variable theory ...
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1answer
51 views

Product of two Pauli matrices for two spin $1/2$

In the lecture, my professor wrote this on the board $$ \begin{equation} \begin{split} (\vec{\sigma}_{1}\cdot\vec{\sigma}_{2})|++\rangle &= |++\rangle \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(\...
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0answers
45 views

Derivation involving finite unitary transformation [closed]

Hi I just want to confirm a short derivation involving a particular finite unitary transformation which is important in QM. My working is as follows: Given the finite unitary transformation defined ...
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0answers
33 views

Changing nature of electrons [duplicate]

At many places I've read about QM, it refers to the change in electron's nature as being a particle and wave at the same time. However, the charged point particle model for the electron still fits ...
4
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2answers
56 views

Heisenberg EOM for $\langle x \rangle$ in momentum eigenstate - where is my error?

Equation of motion for expectation value of a quantum particle in a momentum eigenstate: $$\frac{d}{dt} \langle x \rangle = \frac{1}{i h} \langle [x,H] \rangle$$ and since it's in a momentum ...
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1answer
48 views

Energy conservation and time translations

The time translation is given by a finite unitary transformation $$\hat{U_{\tau}}(\hat{H}) = e^{\big(\frac{i}{\hbar}\tau \bar{H}\big)}.$$ Where $$\hat{U_{\tau}}(\hat{H})|\psi(t) \rangle = |\psi(t-\tau)...
1
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1answer
54 views

Finding the velocity of a given wavepacket [closed]

I've been given a wave packet, that is moving from right to left toward a (known) potential, which has in time $t = 0$ has the form: $$ψ(x, t = 0) = Ae^{−c(x−x_0)^2}e^{ik_0x}$$ and I need to ...
3
votes
1answer
219 views

In quantum weak measurement, what kind of theory replace Copenhagen interpretation?

Here, I denote the initial states of device and quantum system as $|\Phi_\textrm{in}\rangle$ and $|\Psi_\textrm{in}\rangle$. The measurement interval is $[t_i,t_f]$, after measurement, the device and ...
0
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1answer
53 views

Question about Eigenvalues of Hermetian Operators Being Real Numbers

I'm still slogging through Quantum Mechanics: The Theoretical Minimum and I've reached another area that baffles me. Susskind uses the following to show that the eigenvalues of Hermitian operators ...
1
vote
1answer
55 views

Partition sum for $SO(N)$ one-dimensional lattice model

I'm looking for derivation of explicit form of partition function for $SO(N)$ one-dimensional lattice model. The initial expression is $$ Z = \int \limits_{-\infty}^{\infty}d\sigma_{1}...d\sigma_{N}\...
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0answers
30 views

What is the significance of Dirac ortho-normality? [duplicate]

What is the significance of Dirac ortho-normality? We know for momentum eigenfunction $f(p,x)$ for eigenvalue $p$ , $$\langle f(p',x) | f(p,x)\rangle~=~ \delta(p - p') $$ I am not clear why it is ...
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0answers
28 views

Finding the initial state in the power method for Hamiltonian diagonalization

In section III of the lecture note Chapter 1: Exact Diagonalization, Weimer has described the Power method for Hamiltonian diagonalization. The process requires the choice of an random initial state ...
2
votes
1answer
74 views

Why does $\prod^n_{j=1}\sigma^{(j)}_x$ commute with this adiabatic Hamiltonian? [closed]

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. The adiabatic Hamiltonian is defined as $$...
4
votes
1answer
86 views

Ground state of an adiabatic Hamiltonian as an eigenstate of the total spin

I am going through Quantum Adiabatic Evolution Algorithms with Different Paths by Farhi et al. Here, the authors propose to add a special term to the adiabatic Hamiltonian so that the path of the ...
0
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1answer
23 views

Trying to understand Stern-Gerlach filtering problem

I'm attempting to figure out and solve the problems given in my Quantum Physics course below. I would like some clarification on the concept of filtering (relating to questions (ii) to (vi)). From ...
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1answer
44 views

Simple Question about Dirac Notation

Hello I am doing introductory QM and I am getting myself hopefully confused with some Dirac notation. We have that \begin{align*} \langle x' | \psi \rangle &= \langle x' | \hat{I} |\psi \rangle \\ ...
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3answers
385 views

Quantum mechanics on big systems

Looking at this question, I have this related question: there is no doubt that QM gives a very faithful picture of the behaviour of individual particles and atoms. The question is, is there any ...
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2answers
221 views

Can we write the wave function of the living things? If yes then how? [closed]

In quantum mechanics we studied that everything has a wave function associated with it.My question is can we write down the wave functions of things. Then how we can write down the wave functions of ...
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1answer
38 views

how many can we build a set of eigenbasis which describes arbitrary physical system?

Suppose Hamiltonian $H\phi = E\phi$. we can choose eigenstates of Hamiltonian by finding operator $A$ which is $[A,H] = 0$. Does it means that every operator which commutes with $H$ can have same ...
3
votes
1answer
131 views

Confusion About Operators

Hello I am currently studying introductory QM and am confused about bases and operators. If I have an operator $\hat{Q}$, does this represent a change of basis matrix? In other words, does $\hat{Q} | \...
0
votes
1answer
19 views

Why do spectral lines in a series get closer together with increasing frequency?

I thought it would be the other way around, that closer spectral lines meant that the frequency was decreasing and wavelength was increasing. Why is this not the case?
0
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1answer
43 views

Entangled wave function and polarisation operator

I was working on the following problem from Quantum Chemistry and Spectroscopy by T. Engel (3rd Edition), and was stumped in a few places. I wish get some feedback on my solution The problem is the ...
0
votes
1answer
31 views

Norm of quantum state in three dimensions

The Born interpretation states that for a particle with a wave function $\Psi(x)$, the total probability of finding that particle at some point in space is equal to $\int_{-\infty}^{\infty}\Psi(x)^*\...
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votes
0answers
50 views

Books about electomagnetism and quantum mechanics [duplicate]

suggest me some books about electromagnetism. anchor tags:everything about ac,dc circuits,magnetic circuits,semiconductors etc things i need to know through my college years(i am currently doing my ...
0
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0answers
59 views

easy thought experiment for quantum Maxwell demon

I am learning QM,and when I learn tunneling I think of Maxwell demon (I have no thermodynamics backgrounds) Here it goes: There is a potential barrier sitting at x=0 (the whole experiment is 1D) ...
1
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1answer
87 views

Good texts on Quantum Mechanics to accompany this online course [duplicate]

I'm a mathematics undergraduate student and I think of studying QM this summer. I've found two online courses given by professor Fredric Schuller QM (link). I look for a good text that I can use to ...
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1answer
46 views

How can an atom be in an ensemble of energy states?

So I was reading this pdf and in sections 3.2.3 it states theres is an atom with |$\psi_{o}\rangle$ which is a linear combination of two energy eigenstates (a ground |0$\rangle$ and excited state |1$\...
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0answers
40 views

Degenerate perturbations: why is it not necessary that $ [H_0,H']=0$?

Suppose we are doing a degenerate Rayleigh-Schodinger perturbation problem. Let's say the Hamiltonian $H_0$ is perturbed by a small perturbation $H'$, and we want corrections to the energy eigenstates/...
3
votes
2answers
81 views

Understanding operator bra-ket notation

Hi I have a question that might be a bit trivial. I have just completed learning a section on the bra-ket notation. There is a statement that the following is prohibited $$\hat{A}\langle\psi|, ~|\psi\...
0
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1answer
63 views

Number operator in quantum mechanics

In quantum mechanics $a^{\dagger}a$ is defined as the number operator, where $[a,a^{\dagger}]=1$. Why cannot we define $aa^{\dagger}$ as number operator instead of the usual definition?
1
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1answer
36 views

How to find the covariance matrix after a partial homodyne measurement?

The Gaussian state of two modes, with quadrature operators $X_1,P_1,X_2,P_2$, is given by a displacement vector $d$ and covariance matrix $\sigma = \begin{bmatrix} Var(X_1,X1) & Var(X_1,P_1) &...
9
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3answers
569 views

Spacetime and quantum mechanics

In special relativity, the particle has a fixed world line in spacetime. So its whole trajectory is determined. But how can we represent the world line of the particle in spacetime when we take ...
1
vote
1answer
43 views

Is there a connection between the frequency of a photon and the oscillation frequency of the atom which absorbs it?

If a photon has energy $E$, we know it has angular frequency $\frac{E}{\hbar}$. If an atom has an energy gap $E$ between its ground and first excited state, we know that if the atom is in a ...
0
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1answer
46 views

Verification of proof of complete set of commuting operators

Hi I am interested in the validity of the following proof. I am interested in the validity of this particular proof as I am aware of how to prove this result in a different way. Theorem: If two ...
23
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3answers
2k views

Is there an actual proof for the energy-time Uncertainty Principle?

As I understand, the energy-time uncertainty principle can't be derived from the generalized uncertainty relation. This is because time is a dynamical variable and not an observable in the same sense ...
1
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1answer
53 views

Undergraduate quantum book treating density operators, mixed states, and entanglement [duplicate]

I'm working on a project on quantum measurement theory - in particular, relating to the quantum Zeno effect - over the summer. Right now, I'm in the process of doing background readings that'd enable ...
0
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1answer
27 views

What is the relation between adiabatic elimination and adiabatic theorem?

What is the relation between adiabatic elimination and adiabatic theorem? Does adiabatic elimination come from adiabatic theorem?
4
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0answers
134 views

Schrödinger's interpretation of his wave function before Born

The below shows some excerpt from Feynman's lecture notes. 21–4 The meaning of the wave function When Schrödinger first discovered his equation he discovered the conservation law of Eq. (21....
7
votes
3answers
210 views

Can Schrödinger Equation be derived from Huygens' Principle?

Notes of Enrico Fermi start from an analogy between mechanics and optics and with 4 pages he derives the Schrödinger equation. In all my courses, I have seen as an axiom - this is how wave-particles ...
0
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2answers
52 views

Energy of central potential in QM

A hydrogen atom (Coulomb potential) has energy that only depends on $n$ (if we ignore other effects like spin-orbit coupling). In general (not necessarily Coulomb, can be any V), does $E$ depend on ...
0
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1answer
63 views

Quantum entanglement and affecting the particles [duplicate]

I am trying to grasp some aspects of the quantum entanglement, but the existing resources (including some of the links here) seem a bit confusing. I am trying to find an answer to the following ...
3
votes
1answer
29 views

Higher order corrections to hydrogen and their consquence

I was wondering if there have to be higher order corrections for the quantum mechanical description of the Hydrogen atom. I'm aware that there are relativistic corrections and also QED corrections. ...