Quantum mechanics Definition and 994 Threads

I want to study the coherence transfer of the excitation in the FMO complex, so I have to solve the Lindblad master equation. Can I treat my system as a two level system?

There is an interpretation of quantum mechanics out there, and I was not sure if physicists take this seriously, or if it's one of those woo-woo popular misunderstandings of quantum mechanics. So I am posing it to our esteemed physicists here. It says that there can be all sorts of universes...

The non-normalized wavefunction of a general qubit is given by: $$|\psi\rangle=A|0\rangle+B|1\rangle.$$ The complex amplitudes ##A## and ##B## can be represented by two arrows in the complex plane: Now the wavefunction can be multiplied by any complex number ##R## without changing the...

When we think of the fathers of quantum mechanics we tend to think of Max Planck, Albert Einstein, Niels Bohr, Louis de Broglie, Max Born, Paul Dirac, Werner Heisenberg, Wolfgang Pauli, and Erwin Schrödinger. However I think I am in solid ground in suggesting that William Shakespeare was way...

For the case of general potential V(x), what does it mean when he says that there are always one more constraint than free parameters? At each interval, ψ and ψ' must be continuous, so that is 2 constraints at each interval, and I understand that there are 2 parameters of the wavefunction in...

There is a lot of information on the Internet that quantum physics supports solipsism and that physicists believe in solipsism. I only trust this forum and the people who are here, so I want to ask you: 1. Is it true that quantum physics says solipsism is true? If this is true, then only one...

Consider the Schrödinger equation for a free particle: \begin{equation} -\frac{\hbar^2}{2m} \partial_i^2\psi = i\hbar\partial_t \psi. \end{equation} Let us be interested in the motion of a free particle in quantum mechanics. We say ok, we have a solution to the Schrödinger equation for a...

I know how to work through this problem but I have a question on the initial separation of the wave function. Assuming ##\psi(\rho, \phi) = R(\rho)\Phi(\phi)## then for the azimuthal part of the wavefunction we have ##\Phi(\phi)=B\left(\frac \rho\Delta cos\phi+sin\phi\right)##, but this function...

What are some resources that you would suggest for a first course in graduate quantum mechanics? This includes textbooks, online courses such as MIT OCW(includes homework/exams), and online lecture notes?

Background --- Consider the following thought experiment in the setting of relativistic quantum mechanics (not QFT). I have a particle in superposition of the position basis: H | \psi \rangle = E | \psi \rangle Now I suddenly turn on an interaction potential H_{int} localized at r_o =...

I'm a current high school student and I’m aspiring to become a biochemist. I’m at the moment writing an article about adaptive mutations but there is a lot of tricky quantum mechanics in it which I simply don't get. I have asked everyone and got no answer until someone recommended to ask it in a...

My idea was to consider first the structure of the matrix element and to see if there are any possible constraints that we could use for parametrization. If I am not mistaken, we are dealing with the hadronic decay governed by QCD which conserves parity. Since we have a derivative operator...

Travis Norsen in his paper Quantum Solipsism and Non-Locality seems to believe that Everettian QM implies some sort of solipsism. He falls it FAPP (for all present purposes) solipsism. (I must say that as a geologist this goes over my head a bit!) However I have recently read Sean Carrolls...

I have just finished reading the book 'Three Roads to Quantum Gravity' by Lee Smolin. My question interestingly is associated with my geology background. Lee Smolin notes Fay Dowker concludes that if Consistent Histories is true then we cannot deduce the existence of dinosaurs 100 million...

What I tried to do was using the fact that the wave function should be continuous. Asin(kb)=Be^{-\alpha b} The derivative also should be continuous: kAcos(kb)=-\alpha Be^{-\alpha b} And the probability to find the particle in total should be 1: \int_0^b A^2sin^2(kx) dx + \int_b^{\infty}...

My question is the physics behind the LASER such as stimulated emission can be only explained by quantum mechanics only. We can represent LASER as coherent state in quantum mechanics only. Then how can we say LASER can be thought of a classical light source?

I had never heard of Schwinger's Quantum Mechanics: Symbolism of Atomic Measurements until very recently. I wonder what you people think about that QM textbook. Is it a good introduction to QM? A reference? Or, possibly an outdated and bad book? At first glance, it seems a masterpiece to me...

First time posting in this part of the website, I apologize in advance if my formatting is off. This isn't quite a homework question so much as me trying to reason through the work in a way that quickly makes sense in my head. I am posting in hopes that someone can tell me if my reasoning is...

In my book it has the following example, A particle confined to the surface of a sphere is in the state $$\Psi(\theta, \phi)= \Bigg\{^{N(\frac{\pi^2}{4}-\theta^2), \ 0 < \theta < \frac{\pi}{2}}_{0, \ \frac{\pi}{2} < \theta < \pi}$$ and they determined the normalization constant for ##N##...

In the 3rd edition of the Introduction to Quantum Mechanics textbook by Griffiths, he normally does the notation of the expectation value as <x> for example. But, in Chapter 3 when he derives the uncertainity principle, he keeps the operator notation in the expectation value. See the pasted...

hi guys i was thinking about the inner product we choose in quantum mechanics to map the elements inside the hilbert space to real number which is given by : $$\int^{∞}_{-∞}\psi^{*}\psi\;dV$$ or in some cases we might introduce a weight function dependent on the wave functions i have , it seems...

I was wondering if it's possible to plot a wave function that is a function of 3 coordinates, such as (x, y, z). The text my class uses calls this Quantum Mechanics in 3 dimensions, but wouldn't this technically by four dimensions?

Homework Statement:: i saw this simple derivation of the uncertainty principle in my college introductory quantum book Relevant Equations:: Δp.Δx = h hi guys i saw this derivation of the uncertainty principle in my college quantum book , but the derivation seems very simple and sloppy , i...

This is by far the hardest undergraduate class I have ever take. The majority of class got less than 40% on the midterm. Unfortunately, I was sick during the exam hours too ,so it's hard for me to concentrate and think clearly Thank god,the professor uses the norm-referenced grading and My...

In Griffiths Quantum Mechanics 2nd edition, in Chapter 8 he calculates the following integral on page 323 and he gets I disagree with this result, I think the integral should be since Maybe somebody can explain why I am wrong? Also, from equation 8.24 to 8.25, he makes the assumption that...

I'm trying verify the proof of the sum rule for the one-dimensional harmonic oscillator: $$\sum_l^\infty (E_l-E_n)\ | \langle l \ |p| \ n \rangle |^2 = \frac {mh^2w^2}{2} $$ The exercise explicitly says to use laddle operators and to express $p$ with $$b=\sqrt{\frac {mw}{2 \hbar}}-\frac...

Hello everyone, I'm new here and I'm struggling with the mathematical formalities in quantum mechanics. $$\langle n+1|b^\dagger bb^\dagger + \frac 12 |n \rangle = \langle n+1|b^\dagger bb^\dagger |n \rangle + \langle n+1| \frac 12 |n \rangle $$ $$ = \langle n+1|b^\dagger b \sqrt{n+1} |n+1...

I first computed the operator ##\hat{T}## in the ##a,b,c## basis (assuming ##a = (1 \ 0 \ 0 )^{T} , b = (0 \ 1 \ 0)^{T}## and ##c = (0 \ 0 \ 1)^{T}##) and found $$ \hat{T} = \begin{pmatrix} 0&0&1 \\ 1&0&0 \\ 0&1&0 \end{pmatrix}.$$ The eigenvalues and eigenvectors corresponding to this matrix...

I just want to know if Black Holes would be quantumly coherent.

I want to do my Phd on foundations of quantum mechanics, but I don't find researchers in the U.S.A that work on that. Is there a good way to search other than to go to each university and go over the PI's? Thanks

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...