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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3
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1answer
77 views

Feynman propagator for photons and the actual propagation of photons

Reading some books of quantum field theory (c.f. LH Ryder. 'Quantum Field Theory') it seems that the concept of path integrals in quantum mechanics may be extended to the field theory using the ...
3
votes
2answers
123 views

Proton and electron joining

If I have a proton and an electron at rest at some distance apart. Will they form an hydrogen atom when released or they will join together? My intuition says it will form H atom. But I cannot ...
6
votes
2answers
129 views

Are there any true discontinuities in physics?

When we first learn physics, it's often presented very 'discontinuously'. For example, pop quantum likes to talk about objects being "either" particles or waves, leading to a lot of confused questions ...
0
votes
2answers
35 views

Are negative energy eigenstates orthogonal to plane wave states?

Orthogonality in discrete Hilbert spaces is straightforward - those encountered by typical examples of infinite wells of any type, spin systems etc. Continuous Hilbert spaces are fine too - we ...
1
vote
2answers
52 views

Born: matter particle not to be interpreted as wave packet?

In his excellent book "Atomic Physics", after showing that the velocity of a group of waves equals a particle's velocity, Max Born writes that to interpret a particle of matter as a wave packet due ...
0
votes
1answer
44 views

State and measurement after a sequence of measurements

Hi I just want to confirm my interpretation of the following question: Let the quantum state be given as $$|\psi_0 \rangle = [\sqrt{2}|\phi_1 \rangle + \sqrt{3}|\phi_2 \rangle + | \phi_3 \rangle + |\...
0
votes
1answer
24 views

Why is collision of electrons different from alpha particles in terms of probability amplitude?

In The Feynman lectures on physics volume 3, chapter 3, page 3-11, there is the following paragraph: An even more perplexing thing happens when we do the same kind of experiment by scattering ...
-3
votes
0answers
29 views

How long should an Observer measure to find an electron near Hydrogen nucleus?

I was wondering whether the following question makes sense: A probe is put near the Bohr radius of Hydrogen nucleus.The probe covers a region dV(small volume). The probe may or may not find the ...
0
votes
1answer
31 views

Does an odd potential commute with parity operator?

I can prove when a Hamiltonian commute with the partity operator if the potential is even. But what about an odd potential? my understanding is that the parity operator mirrors the coordinate system, ...
-1
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0answers
42 views

Observer effect quantum physics [duplicate]

In the Observer Effect in quantum physics if observation collapses the waveform into a particle how come you bump into things in the dark where you havent observed them at all!?
0
votes
2answers
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
votes
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
votes
2answers
104 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
votes
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 ...
0
votes
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 ...
0
votes
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 $2^N$. ...
0
votes
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 ...
1
vote
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?
-1
votes
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 ...
1
vote
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 \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(\...
1
vote
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 ...
-5
votes
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
votes
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 ...
1
vote
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
vote
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
votes
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}\...
0
votes
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 ...
0
votes
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
votes
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 ...
0
votes
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 \\ ...
7
votes
3answers
386 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 ...
0
votes
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 ...
-2
votes
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
votes
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)^*\...
-4
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
votes
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
vote
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 ...
-1
votes
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$\...
0
votes
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
votes
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
vote
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
votes
3answers
570 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 ...