Quantum mechanics Definition and 994 Threads

I'm just starting my undergraduate Quantum Mechanics course. I had a homework problem to show that \Delta S_x = \sqrt{\langle S_x^2 \rangle - \langle S_x \rangle ^2} = 0 , S_x being the spin in the x direction. I managed to solve it, but the physical interpretation is confusing me. If I...

I learned that the energy operator is ##\hat{E} = i\hbar \frac{\partial}{\partial t} ## and the Hamiltonian is ##\hat{H} = \frac{-\hbar^2}{2m}\nabla^2+V(r,t)## If the Hamiltonian represents the total energy of the system. I expect the two should be the same. Did I misunderstand the concept of...

In this article [1] we can read an explanation about Wilson's approach to renormalization I have read that Kenneth G Wilson favoured the path integral/many histories interpretation of Feynman in quantum mechanics to explain it. I was wondering if he did also consider that multiple worlds...

A member helped me discover a new quantum tunneling sim online, it's free and quite amazing to look at. https://phet.colorado.edu/en/simulation/quantum-tunneling Are there any other more advance simulators on the net and would anyone like to discuss this program with me as I am new to Quantum...

Hi everyone , I am interested in learning quantum mechanics. I want to read a book which explains each and every aspect of quantum physics , gives a conceptual understanding with the help of logical thinking. Also it should be like that if I know the most basic theory and...

Given that the Minkowski metric implies the Lorentz transformations and special relativity, why do the equations of relativistic quantum mechanics, i.e., the Dirac and Klein-Gordon equations, require a mass term to unite quantum mechanics and special relativity? Shouldn't their formulation in...

Reading book, “God? Very Probable”. The author quotes Wigners comments in his book, “Remarks on the Mind- Body Question” 169, 171, 173. “The very study of the external world led to the conclusion that the content of consciousness is an ultimate reality. Given the ultimate priority of...

I have a basic question in elementary quantum mechanics: Consider the Hamiltonian $$H = -\frac{\hbar^2}{2m}\partial^2_x - V_0 \delta(x),$$ where ##\delta(x)## is the Dirac function. The eigen wave functions can have an odd or even parity under inversion. Amongst the even-parity wave functions...

After getting the values of ψ₀(x) and ψ₁(x), I put them in the expression of ϕ(x) to get: ϕ(x) = (mw/πℏ)^(1/4) * exp[-(mw/2ℏ)x^2] * [α + βx√(2mw/ℏ)] Now when attempting to find the value of <x> by ∫xϕ(x) dx, I am having trouble determining the limits, as I am getting nothing useful by...

So according to Heisenberg's energy-time uncertainty principle, the product of accuracies in energy and time is equal to ћ/2. In this problem, I know I have to calculate ΔE. But when I'm using Δt = 1.4e10 yrs. = 4.41e17 s, I am getting ΔE = 0.743e-33 eV, which is certainly incorrect! Where am I...

I'm wondering if this would be a way to interpret the double slit experiment. In other words, when we observe an electron in the present, it goes through one slit or the other as a particle. However, if we do not observe it, it goes through both at once as a wave; we only see evidence of it...

Please critique this text. It came from a research article* I found but I'm only interested if the sentence is 100% accurate or not and not in the specifics of the article itself. Are they suggesting Hilbert space is always infinite? Thanks. Quantum mechanics is infinitely more complicated than...

According to the Many Minds interpretation of quantum mechanics (https://en.wikipedia.org/wiki/Many-minds_interpretation), the distinction between worlds in the Many Worlds interpretation should be made at the level of the mind of an individual observer. I have read that, in this case, each...

Hi All, I've been going through Shankar's 'Principles of Quantum Mechanics' and I don't quite understand the point the author is trying to make in this exercise. I get that this wavefunction is not a solution to the Schrodinger equation as it is not continuous at the boundaries and neither is...

I think Weinberg is quite clear about this: On p.87 of the second edition of his quantum mechanics book, he says, and on p.88: After having discussed decoherence, he says on p.92: For the instrumentalist approach (apparently your view of the matter), he states on p.92f this drawback: Then...

In quantum mechanics, we have the partition function Z[j] = e-W[j] = ∫ eiS+ jiOi. The propagator between two points 1 and 2 can be calculated as ## \frac{\delta}{\delta j_1}\frac{\delta}{\delta j_2} Z = \langle O_1 O_2 \rangle## The S in the path integral has been replaced by S → S + jiOi...

Hello guys, I struggle with one step in a calculation to show a quantum operator equality .It would be nice to get some help from you.The problematic step is red marked.I make a photo of my whiteboard activities.The main problem is the step where two infinite sums pops although I work...

Hey, applied maths and physics student here. I started wondering recently what the meaning of measurement was in quantum mechanics, and I remembered that I had once heard of the bohmian interpretation which challenged the impression I had so far (which was that hidden variables had been...

I'm interested in a book which treats scattering in quantum mechanics aimed at the research-level. I'm particularly interested in a text which focuses on mathematical details such as the analytic structure of the S matrix, the relation between the S matrix and various green's/two-point...

As a quarantine hobby I've been learning about Grete Hermann and the early history of QM. I find her early philisophical contribution to be interesting, but I lack the background to put it into a modern context. A brief description can be found in the arxiv paper: Grete Hermann: An early...

May i know how do i eliminate C and D and how do i obtain the last two equations? Are there skipping of steps in between 4th to 5th equation? What are the intermediate steps that i should take to transit from 4th equation to the 5th equation?

In the context of non relativistic quantum mechanics, or better, if I consider the neutrino's mass to be zero, the phrase seems to me puzzling. What I know is that if I know the direction of motion, I know the spin projection onto that direction, say ##\hat{z}##-direction. But to not violate...

I can not solve this problem: However, I have a similar problem with proper solution: Can you please guide me to solve my question? I am not being able to relate Y R (from first question) and U (from second question), and solve the question at the top above...

is my solution correct?

This is a general property of eigenvectors of Hermitian operators. State functions are a particular class of vector, and it is easiest to work in the general formalism (I am hoping to show how ket notation makes qm easier, not just do standard bookwork at this level). Suppose O is a Hermitian...

A relativistic origin of QM is proposed in https://iopscience.iop.org/article/10.1088/1367-2630/ab76f7 It is proposed that lorentz transformation that include superluminal observers (whether those observers exist or not) explain the indeterministic behavior of QM. Not only that, it also would...

I need help .I did not A) E < V0 for T =? (passing coefficient ) B) E = V0 for T = ? C ) E > V0 for T =? A

In quantum mechanics in books authors discuss only cases ##E<V_0## and ##E>V_0##, where ##E## is energy of the particle and ##V_0## is height of the barrier. Why not ##E=V_0##? In that case for ##x<0## \psi_1(x)=Ae^{ikx}+Be^{-ikx} and for ##x\geq 0## \psi_2(x)=Cx+D and then from...

I was learning about Degenerate Perturbation Theory and I encountered the term 'Degenerate Subspace', I didn't really understand what it meant so I came here to ask - what does it mean? will it matter if i'll say 'Degenerate space' instead of 'Degenerate Subspace'? and subspace of what? (...

In R Shankar text on “principles of quantum mechanics’ discussing the adjoint operation, 1.3.8 shows that a|V> => <V|a*. Then 1.3.9 then states that <aV| = <V|a*. Is this a typo error?

How do "sinϕ - cosϕ sinϕ" become 0 ?

Summary:: Linear Quantum harmonic oscillator and expectation value of the potential energy (time dependent) Hello, I have attached a picture of the full question, but I am stuck on part b). I have found the expectation value of the <momentum> and the <total energy> However I am struggling with...

Homework Statement:: 1. Does the increase in kinetic energy in (for example) water that results from increasing its temperature result from electron excitation (i.e. increasing electron energy levels) or simply increasing their velocity or vibration amplitude/frequency? 2. If excitation is...

Fermilab's Don Lincoln describes Quantum Entanglement, and how it is different from classical statistics and hidden variables scenario.

Hello, I am struggling with what each piece of these equations are. I generally know the two rules that need to hold for an operator to be linear, but I am struggling with what each piece of each equation is/means. Lets look at one of the three operators in question. A(f(x))=(∂f/∂x)+3f(x) I...

https://www.nature.com/articles/d41586-020-00120-6

I'm self studying so I just want to ensure my answers are correct so I know I truly understand the material as it's easy to trick yourself in thinking you do! A particle of mass m is in a 1-D infinite potential well of width a given by the potential: V= 0 for 0##\leq## x ##\leq## a =...

According to Nobel laureate Frank Wilczek, the universe emerges from a Grid. This was proposed in his book "The Lightness of Being: Mass, Ether, and the Unification of Forces". He also likes the idea that the universe emerged from a state of "nothingness" (or rather, a quantum vacuum) where...

In 1935, Austrian physicist Erwin Schrödinger was looking at a concept called a "superposition." Superposition is when two waves meet and overlap and interact, which can lead to different results based on the circumstances. The concept can be seen in the regular-sized world as well, in...

In Quantum Mechanics, by Wigner's theorem, a symmetry can be represented either by a unitary linear or antiunitary antilinear operator on the Hilbert space of states ##\cal H##. If ##G## is then a Lie group of symmetries, for each ##T\in G## we have some ##U(T)## acting on the Hilbert space and...

I don't quite understand how he got the line below. By using discrete time approximation, we can get the second order time expression. But i don't see how by combining terms he is able to get such expression.

In the Many Worlds Interpretation's wikipedia article (https://en.wikipedia.org/wiki/Many-worlds_interpretation), it says, at the "Reception" part: "(...) On the other hand, the same derogatory qualification "many words" is often applied to MWI by its critics, who see it as a word game which...

hello! I've been trying to read through Sakurai's Modern quantum mechanics textbook ( My goal is to finish the first 3 chapters and understand the Dirac formulation of QM specifically) but I find myself stumbling at many places. Are there any video lectures on the internet that follows this text...

I'm considering a hydrogen atom placed in an infinite potential on one side of the nucleus, i.e. ##V(x) = +\infty## for ##x < 0##. I require the wavefunctions to be odd in order to satisfy the boundry condition at ##x=0##. By parity of the spherical harmonics only states with ##l## odd are...

Did Schrödinger believe that contradictory or inconsistent things could exist in reality?

This should be a trivial question. I am trying to compute the spherical tensor ##T_0^{(0)} = \frac{(U_1 V_{-1} + U_{-1} V_1 - U_0 V_0)}{3}## using the general formula (Sakurai 3.11.27), but what I get is: $$ T_0^{(0)} = \sum_{q_1=-1}^1 \sum_{q_2=-1}^1 \langle 1,1;q_1,q_2|1,1;0,q\rangle...

I have insertet the equations for H and P in the relation for the commutator which gives $$[H,P] = [\sum_{n=1}^N \frac{p_n^2}{2m_n} +\frac{1}{2}\sum_{n,n'}^N V(|x_n-x_n'|),\sum_{n=1}^N p_n] \\ = [\sum_{n=1}^N \frac{p_n^2}{2m_n},\sum_{n=1}^N p_n]+\frac{1}{2}[\sum_{n,n'}^N...

Hi everyone! This is the first time I'm posting on any forum and I'm still rather unsure of how to format so I'm sorry if it seems wonky. I'll try my best to keep the important stuff consistent! I am working on infinite square well problems, and in the example problem: V(x) = 0 if: 0 ≤ x ≤ a...

I have tried doing the obvious thing and multiplied the vectors and matrices, but I don't see a way to rearrange my result to resemble the initial state again: ##(\mathcal{D_{1y}(\alpha)} \otimes \mathcal{D_{2y}(\alpha)} )|\text{singlet}\rangle = \frac{1}{\sqrt{2}}\left[ \begin{pmatrix}...

Suppose I have a positive spin-##1/2## eigenstate pointing in the ##z##-direction. If I apply a rotation operator by an angle ##\theta## around the ##z##-axis the state should of course not change. However, if I write it out explicitly, I find something different: $$R_z(\theta)|\uparrow\rangle =...