Qm Definition and 1000 Threads

In Matthew Schwartz's QFT text, he derives the Schrodinger Equation in the low-energy limit. I got lost on one of the steps. First he mentions that $$ \Psi (x) = <x| \Psi>,\tag{2.83}$$ which satisfies $$i\partial _t\Psi(x)=i\partial_t< 0|\phi...

Electrons' spin state is responsible for magnetism inside a magnet. Two magnets interact at a distance, but what about the space between and around the two magnetic objects? In CM there are field lines and vector fields, but what is actually happening at the QM level?

This thread is a shootoff from this post in the thread Summary of Frauchiger-Renner. The topics are related, but this thread offers a new perspective that diverges from the main subject of that thread. In QM foundations, the sheer amount of interpretations, disagreement among experts about what...

I'm a hobbyist physicist and I just started studying QM through watching Leonard Susskind's lectures on the Stanford Youtube channel. I get the idea of it being impossible to precisely know both a subatomic particle's position and momentum, but is this actually a physical limitation? Or is it...

Hi, Two questions. Are Weinberg's "Lectures on Quantum Mechanics" a bridge to his QFT books? I read that his QFT volumes are excellent books, but not for the beginner. So, if I want to begin QFT, can I choose his "Lectures on Quantum Mechanics" for a graduate level QM book, and make the...

Hi all! Happy New year! I will select my supervisor soon but i want to involve in the field that uses QM or GR frequently I love physics and i want to apply physics to explain astrophysical phenomenon. I know that Compact objects and Astrochemistry use such physics but i wonder to know more...

Homework Statement Consider an electron in a hydrogen atom in the presence of a constant magnetic field ##B##, which we take to be parallel to the ##z##-axis. Without the magnetic field and ignoring the spin-orbit coupling, the eigenfunctions are labelled by ##\vert n, l, m, m_s \rangle##...

Homework Statement Question attached : Just number 1 please Homework Equations Hamiltonian is given by eq ? In the attachment ##\phi(x_1,x_2,...x_n,t)= \int dx_1...dx_n \phi(x_1,x_2...x_n,t) a^+(x_1)...a^(x_n) |0> ## Where ## |0> ## is the vacuum state and ##a(x) |0>=0## The Attempt at a...

Homework Statement This isn't exactly a problem but rather a problem in understanding the derivation of the phenomenon, or more precisely, one step in the derivation. In the following we will consider the EPR pair of two spin ##1/2## particles, where the state can be written as $$ \vert...

Homework Statement Consider a 2-particle system where the two particles have angular momentum operators ##\vec{L}_1## and ##\vec{L}_2## respectively. The Hamiltonian is given by $$H = \mu\vec{B}\cdot (\vec{L}_1+\vec{L}_2)+\gamma \vec{L}_1\cdot \vec{L}_2.$$ Determine explicitly the eigenvalues...

Let's say I have a system whose time evolution looks something like this: This equation tells me that if I measure energy on it, I will get either energy reading ## E_0 ## or energy reading ## E_1 ## , when I do that, the system will "collapse" into one of the energy eigenstates, ## \psi_0 ##...

There are two recent threads about the subject, however I want to ask a different question. What does the wavefunction is "real" imply or what such "clarification" actually mean to the deeper understanding of QM. The theory is purported to be revolutionary and important breakthrough, yet it...

Homework Statement Let ##U_t = e^{-iHt/\hbar}## be the evolution operator associated with the Hamiltonian ##H##, and let ##P=\vert\phi\rangle\langle \phi\vert## be the projector on some normalized state vector ##\vert \phi\rangle##. Show that $$\underbrace{PU_{t/n}P\dots PU_{t/n}}_{n\text{...

Homework Statement Prove that the Clebsch-Grodan coefficients (in the notation ##\langle j_1j_2m_1m_2|j_1j_2jm\rangle##) for the decomposition of the tensor product of spin ##l## and spin ##1/2## to spin ##l+1/2## are $$\left\langle l,\frac{1}{2},m\mp \frac{1}{2}, \pm \frac{1}{2} \Bigg\vert l...

I understand photons and elections fit into the probalistic rules of QM. Are there any other elementary particles (more massive) that don’t obey the point/wave duality?

A long time ago, someone told me that Einstein thought spacetime is "smooth and continuous." Quantum mechanics is a proven fact. Quantum mechanics exists in spacetime, though. So can we at least conclude that spacetime is not continuous, and instead discrete? ...quanta of space and time...

Much as the title of this thread asks: does quantum mechanics use n-dimensional or infinite dimensional integrals? I'm merely curious as I studied the n-dimensional case as a hobby and wondered if I'd ever get to use it for anything cool like QM. If so, please maybe post one such integral so I...

hi! Do you know about a good book that introduces relativistic quantum mechanics with one-forms (diferential forms) like the book a first course of general relativity of Schutz does?

In Classical Mechanics, according to SR, the concept of simultaneity is dead, a meaningless concept. But in QM, entanglement implies that some limited form of simultaneity exists. If we have two particles correlated due to entanglement, a measurement of one particle immediately gives us the...

Math definition: integral of function within limits divided by difference of limits. QM definition: integral of complex conjugate of wave equation times function times wave equation within limits of minus to plus infinity.

Homework Statement Consider the following ket: |ψi> = c1|e1> + c2|e2>, where ci are some complex coefficients. Find the column-vector representation of |ψi> in the |ei> basis. Find the row-vector representation of <ψ| in the <ei| basis. Homework Equations |ψi> = c1|e1> + c2|e2> The Attempt at...

I know this has been discussed in so many ways on this forum, but it is hard for me to separate interpretations, fact, speculation, and inaccuracies. You can probably just skip the next two paragraphs that I describe the EPR/Aspect experiment and go right to my question. In an EPR experiment...

Work in quantum foundations is partly considered important because of the hope that the way we think about QM may point to a road to quantum gravity. Lucien Hardy, who is well-known in quantum foundations for his reformulation of QM in terms of five "reasonable" axioms, is one of the people who...

Homework Statement I wish to solve this integral $$b_{lm}(k) = \frac{1}{2(\hbar)^{9/4}(2\pi)^{5/2}\sqrt{\sigma_{px} \sigma_{py} \sigma_{pz}}} \int_{\theta_k = 0}^{\pi}\int_{\varphi_k = 0}^{2\pi} i^l \text{exp}\left[ - \frac{1}{(2\hbar)^2}\left(\frac{(k_z - k_{z0})^2}{\sigma_{pz}^2} + \frac{(k_y...

I decided to go deep in physics theories such as QFT, general QM and Special/General Relativity. Would it be better to spend a lot of time, say, 1+ year, learning through the most complete math books or just use books that mix math and physics to learn the necessary and suficient math and go to...

When talking about measurement in QM it's completely normal to think right away about someone doing "something" to get or "observe" a definite quantum state... ...but how about the screen in a standard DS? ...there we get clumps if we measure a quantum state at the slits or fringes if not...

Why from Φ eq in page 136, he did not derive the solution in this form $Ae^{imφ}+Be^{-imφ}$https://drive.google.com/open?id=1thokDDIVDytck1-2HI3qyiG07mAMO1nc

I cannot understand this excerpt from a book on quantum mechanics with reference to observables. I understand that the orthogonality theorem causes all values except the "equal" values lead to zero.However what do they mean when they say "if the integrand is finite the integral (29)...

Consider this a layman's question. I am not an expert on deeper aspects of probability. I simply rely on Kolmogorov's axioms and the calculation methods I learned as a student. To me it's just a bit of mathematics and it makes perfect sense as mathematics. When it comes to actually...

At my school, you have to take Quantum mechanics at the same time as Statistical mechanics (co-requisites) in either junior or Senior year as a physics major; why is this? What is the relationship between the 2?

Hey there! While considering going into foundational issues in QM (reading abou entanglement and Bell's theorems now), I realized I may need a better grasp of QM. I have studied both Griffiths' and Cohen-Tannoudji's (both volumes, excluding the appendices) books. I am not very confident in my...

It seems to me that so far in quantum mechanics, because we have yet to establish probability patterns for, say, what the spin of a photon is, we have made it some mystical thing that we can only know by measuring it. I don't really buy that; is the result of a lottery impossible to know until...

Homework Statement Hello, This is not a homework help problem but I believe this question belongs here more so than in the other forums. I would like to (for personal benefit) duplicate / generate the plots in Figure 2.6 of Griffiths Quantum Mechanics book - page 55, 2nd edition. Homework...

Homework Statement Hi, I was reading Griffiths and stumble upon some questions. This is from 5.1.2 Exchange Forces. The section is trying to work out the square of the separation distance between two particles, $$\langle (x_1 - x_2)^2 \rangle = \langle x_1^2 \rangle + \langle x_2^2 \rangle -...

I am trying to read about and understand string theory. But in trying to understand how it reconciles with the world of quantum field theory and quantum mechanics, I am getting a little confused. How does the string move through and propagate through the quantum field? Does string theory...

I know quantum mechanics meeting with general relativity or quantum gravity is a difficult work to do.　In order to understand the problem more, I would like to know about QM in virtual gravity, e.g. Rindler system or rotating system. Is wave function in rotation system is fully derived, for...

Hi physics forms! I'm practicing to for an Quantum mechanics exam, and i have a problem. 1. Homework Statement I have two problems, but it's all related to the same main task. I have a state for the Hydrogen: ## \Psi = \frac{1}{\sqrt{2}}(\psi_{100} + i \psi_{211})## where ## \psi_{nlm}##...

Hello there, So I just finished a course on Qm with Griffiths but the teacher was not the best, to say the least. I disliked the book too and its kind of childish or funny way of presenting stuff. During the summer break I want to go over QM again but with a better book and by myself. I loved...

If we use a probabilistic model of QM, is there still room for determinism? If we don't have knowledge of the exact outcomes, can there still be underlying determinism in such a model? I am aware there are probabilistic and deterministic models available for QM. Does that mean QM could be...

I was reading this paper https://arxiv.org/pdf/0805.4725.pdf It seems that the potential between the particles can be assumed of different forms, shouldn't the potential be a solution of the problem. Thanks

I read this wiki and some of the references https://en.wikipedia.org/wiki/Bound_state But I can't really understand. For example the electron in hydrogen has specific energies and not general relations that the articles seem to claim. Thanks

Homework Statement A particle is represented by the following wave function: ψ(x)=0 x<-L/2 =C(2x/L+1) -L/2<x<0 =C(-2x/L+1) 0<x<+L/2 =0 x>+L/2 use the normalization condition to find C Homework Equations ψ(x) must be...

Homework Statement Question attached: Homework Equations below The Attempt at a Solution I have completed this question and the needed commutator relation is that ##[a(x),a^+(x')]=\delta(x-x')## However I have it all with the integral i.e. ##\int dx_1 dx_2 a^+(x_1)a^+(x_2) \Psi...

I mean the equation shows the particle could have any momentum, how did that came about. If it is truly free it should have only an energy of mc^2, shouldn't it.

In non-relativistic QM, given a Hilbert Space with a Hermitian operator A and a generic wave function Ψ. The operator A has an orthogonal eigenbasis, {ai}. I have often read that the orthogonality of such eigenfunctions is an indication of the separateness or distinctiveness of the associated...

Homework Statement specific lagrangian is defined. Have to get a equation of motion Homework Equations [/B] Lagrangian is defined as The Attempt at a Solution [/B] eq of motion that i drive like i guess term of f(x) have to vanish or form a shape of curl. but it didn't be clear...

[Moderator's note: This discussion has been spun off from another thread since it was getting into a more technical area only tangentially related to the original thread's topic. Some posts have been edited slightly for the new context.] They're too technical for the question here, and only...

Homework Statement Question attached here: I am just stuck on the first bit. I have done the second bit and that is fine. This is a quantum field theory course question but from what I can see this is a question solely based on QM knowledge, which I've probably forgot some of. Homework...

Homework Statement A particle is moving in a 1-dimensional harmonic osciallator with the hamiltion: ## H = \hbar \omega (a_+ a_- + \frac{1}{2})## at time ## t=0## the normalized wave function is given by ## \Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x) + i\psi_1(x)) ## Task: Calculate for ## t \geq...

Homework Statement A particle is moving in a one-dimensional harmonic oscillator, described by the Hamilton operator: H = \hbar \omega (a_+ a_- + \frac{1}{2}) at t = 0 we have \Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x)+i\psi_1(x)) Find the expectation value and variance of harmonic oscillator...