Quantum mechanics Definition and 994 Threads

Hello, I was just wondering if there is a geometric interpretation of the trace in the same way that the determinant is the volume of the vectors that make up a parallelepiped. Thanks!

What is the difference between these reduced Planck masses? ##M_p = \sqrt \frac{ħc}{8πG}~## and ##~M_p = \sqrt \frac{1}{8πG}## I see people use either, but what is the difference? It can't be that ħ and c are set to 1 because G is also a Planck unit and it would be nonsense to set a Planck...

Lately I've taken a lot of interest in quantum mechanics but I have no formal schooling on the topic. Actually I dropped out of high school and joined the army, so besides using a map and compass or counting ammo I've had barely any use for math at all in about 10 years. But I've enjoyed quite a...

So I whilst understanding basics of some quantum phenomena like superposition, tunnelling, fluctuations etc I happened to watch the movie "Coherence" where there's a scientifically unsatisfactory reference to quantum decoherence. What exactly is this concept?

I'm interested in learning Quantum Mechanics the way it was discovered, and that seems to be from blackbody radiation, which itself seems to be first quantified by Wien's Displacement Law. So Wikipedia says Wien derived this law by "considering adiabatic expansion of a cavity containing waves...

The books are based on Schwinger's but is much easier read. Uses my favorite spins-first approach. Lectures On Quantum Mechanics vol. 1, 2, & 3 by Berthold-Georg Englert https://www.amazon.com/dp/9812569715/?tag=pfamazon01-20 https://www.amazon.com/dp/9812569731/?tag=pfamazon01-20...

I recently found that formulation of quantum mechanics as a hamiltonian flow in a Kahler manifold, where there is a classical hamiltonian, hamilton equations, poisson brackets and etc. And while the mathematics in terms of differential geometry is all fine and good, I'm having problem finding...

Homework Statement We describe particle's movement with the Hamiltonian: H=- \frac{\Delta E}{2} |0\rangle \langle0| + \frac{\Delta E}{2} |1\rangle \langle1|, where |0\rangle and |1\rangle are the ortonormal basis. Let: |a\rangle = \frac{1}{\sqrt{2}}|0\rangle +\frac{i}{\sqrt{2}}...

As I understand it (e.g. from discussions around the Fermi field theory of the nuclear force), a spin 1/2 particle can emit a spin-1 particle and simultaneously flip its spin (say, spin +1/2 -> photon +1 & spin -1/2); but how does this work with spin-2 particles? Does it need to emit pairs in...

I am a retired Physicist (Ph.D. U of NM 1977 in Astrophysics) who has spent most of his working life as a systems engineer and computer modeler. I now video conference Fridays with 4 friends to talk about the things we learned to calculate in grad school, but were never quite got the reason...

Hello! I just started reading about SU(2) (the book is Lie Algebras in Particle Physics by Howard Georgi) and I am confused about something - I attached a screenshot of those parts. So, for what I understood by now, the SU(2) are 2x2 matrices whose generators are Pauli matrices and they act on a...

My intuition tells me that it does not given that physical phenomena don't obey the principle of sufficient reason under quantum mechanics (a dogma many still hold certain). A lucid definition of the PoSR can be found here. Meaning, that some events are non-localized and the distinction between...

I heard from many sources that quantummechanics is purely random in nature. Has this been demonstrated? If so, what is the proof?

Hello, When we normalize the free particle by putting it in a box with periodic boundary conditions, we avoid the "pathological" nature of the momentum representation that take place in the normal problem of a particle in a box with the usual boundary conditions of Ψ=0 at the two borders. Thus...

Why is 'quantum physics' often referred to as 'mechanics'? I'm interested in the specific origin of the term - when it came into vogue, and why 'mechanics' was thought suitable as a term, when it doesn't seem at all obvious that the subject matter involves mechanical principles.

Hello, I have used Greiner's "Quantum Mechanics: An introduction" and found it to be awesome, bridging the ga between undergraduate and graduate courses. So, I am thinking of buying some of Greiner's book to use for my other courses and I wanted to ask you what your opinions about the books in...

Homework Statement In Griffiths Introduction to Quantum Mechanics textbook, he shows that for any wave function that is time-dependent (which implies that the state of any particle evolves with time), the wave function will stay normalized for all future time. There is a step in the proof that...

Heisenberg's uncertainty principle: due to experimental limitations or dual nature of matter? Or both?

I'm just being introduced to quantum mechanics and physics, and I was wondering if the possibility of a parallel universe could exist. And if so, how do we know? I read some articles about the research done with Australian researchers who theorize that parallel universes do exist and interact...

While studying Ehrenfest's theorem I came across this formula for time-derivatives of expectation values. What I can't understand is why is position/momentum operator time-independent? What does it mean to be a time-dependent operator? Since position/momentum of a particle may change...

I am an undergraduate student in India doing my final year BS degree in Math. I am extremely interested in quantum mechanics and want to peruse quantum computation. What is the best possible course that I can take for my Masters? There appears to be a limited number of colleges that offer a...

If so, how.

Hello guys, I just finish my first year at uni Phys and Maths,and would like to self teach Quantum Mechanics during this summer, as so I was wondering if you guys could suggest me any good full online courses/ lectures available on the web . I have found from neptel from Oxford Bookwise...

So I've always been fairly good at whatever science I learned in elementary and middleschool (which was mostly biology), and I've fairly enjoyed it, but I've only recently started really learning, and I've come to love it. I've especially found quantum physics interesting, however, seeing as I...

Homework Statement Reading Sakurai I cannot see how he gets to the end of 1.7.15 as below: Homework Equations ∫dx'|x'><x'-dx' |α> = ∫dx'|x'>{<x' |α>-Δx'∂/∂x'<x' |α>} The Attempt at a Solution I tried a Taylor expansion but cannot see how this is derived.

I want to study quantum mechanics for undergrad level, and found out really lots of people recommends "Introduction to Quantum Mechanics by David J.Griffiths" which is Alright, so I visited my school book store for this cat-pictured book. and found this puzzle-pictured book. Same name same...

Homework Statement Exercise 4 in the upload titled Dok1.pdf. Write down an expression for the canonical partition function for N ideal Na2 gas molecules, when the rotational contribution is treated classically, and all inner degrees of freedom are treated quantum mechanically. Use this and...

It would be really appreciated if somebody could clarify something for me: I know that stationary states are states of definite energy. But are all states of definite energy also stationary state? This question occurred to me when I considered the free particle(plane wave, not a Gaussian...

Hello! Could somebody please tell me how i can compute the expectation value of the momentum in the case of a free particle(monochromatic wave)? When i take the integral, i get infinity, but i have seen somewhere that we know how much the particle's velocity is, so i thought that we can get it...

Hello! I am reading something about applications of group theory in quantum mechanics and I got confused about the difference between direct sum and direct product. In many places I found that they mean the same thing. However, the ways I found them defined in the book I read from, seem to be...

I have read several times that general relativity has some problems with quantum mechanics and they are not compatible. However, special relativity can be introduced in quantum mechanics mainly by Dirac equations (so I am pretty sure that the problem of passing from a frame where the parameter...

Hi All, Once in the past I have heard that the vacuum in quantum mechanics, having its energy given by ## \sum_n \frac{1}{2}\hbar \omega_n ## was also obtained by methods of Einstein's relativity, through the claim that the vacuum should be a field which is invariant under a boost...

Hi, I just completed my second year of my physics undergraduate degree. And recently did a course on Quantum Mechanics. I have a few questions regarding the basic theory and postulates, probably, because due to lack of full clarity. So, Consider a wave function ψ(x,o), which is well behaved and...

What is the role of Quantum Mechanics and Thermodynamics in solar cell operation? Is quantum mechanics the photovolatic effect, and thermodynamics the cell efficiency?

In classical mechanics we use a 6n-dimensional phase space, itself a vector space, to describe the state of a given system at anyone point in time, with the evolution of the state of a system being described in terms of a trajectory through the corresponding phase space. However, in quantum...

One of the greatest quest in physics is to reconcile Relativity with QM. But is this reconciliation really necessary? They both work quite well in their respective fields so why not just leave it at that? The only issue I can see is the problem of the singularity but can't that be solved by...

Hey Everyone, Question about time reversibility. In considering the reversibility of a system over an interval of time, shouldn't it be put into consideration, that because all interactions were random, that if one were to somehow "go back in time" or reverse the process, that the initial...

Homework Statement I am watching a course on Relativistic Quantum Mechanics to freshen up, and I have found to have some issues regarding simple operator algebra. This particular issue on the Pauli Equation (generalization of the Schrodinger equation that includes spin corrections) in an...

Homework Statement Hi! I'm writing my lab report on the Franck-Hertz experiment and I have trouble with the contact potential difference (inelastic collision). How do you calculate it? Homework Equations See below The Attempt at a Solution The energy differences between the maximum and...

There seems to be two divided approaches in how the uncertainty principle is explained, but they seem to be explaining two different things. The first, more intuitive explanation of the limits imposed by quantum mechanics goes something like: in order for a measurement to be made, we have to...

Homework Statement Hi! I have a a question regarding the Atomic Spectra of Hydrogen and Mercury. My problem involves the value of m and Rydberg's constant. I used a spectrometer for this lab and calculated all the necessary angles. Homework Equations See below The Attempt at a Solution...

Upon searching in this forum, i have found discussions about the standard undergraduate textbooks on QM not being so good in teaching you the foundations properly. A good example is the difference between Hermitian and self-adjoint operators. Some people are saying that we should study QM from a...

I have read that the Schrodinger Uncertainty Principle is an extension of Heisenberg's. So, why don't we use the Schrodinger Uncertainty Principle instead of Heisenberg's? Thanks!

In the Infinite Square Well problem, an energy eigenstate is in an equal superposition of two momentum eigenstates with eigenvalues that are opposite in sign(like standing waves that are formed by two wavefunctions corresponding to "opposite momentums"). So, for every energy eigenstate, we...

The overall problem is to prove that [L^2,[L^2,\hat{r}]]=2\hbar^2 {L^2,r} I feel I am very close to solving this problem but I need a quantum version of the vector identity ax(bxc). Because the relevant vectors are operators that don't commute, there is a problem. Does anybody know of a source...

Consider a system of two identical spin-1 particles. Find the spin states for this system that are symmetric or antisymmetric with respect to exchange of the two particles. (Problem 13.3, QUANTUM MECHANICS, David H. McIntyre) I know that for bosons, the total wavefunction should be symmetric...

Hello, i am kind of confused about something. What is the complex conjugate of the momentum operator? I don't mean the Hermitian adjoint, because i know that the Hermitian adjoint of the momentum operator is the momentum operator. Thanks!

According to one of the postulates of quantum mechanics, every measured observable q is an eigenvalue of a corresponding linear Hermitian operator Q. Which means, that q must satisfy the equation Qψ = qψ. But according to Griffiths chapter 3, this equation can only be followed from σQ = 0. It...

If one has two single-particle Hilbert spaces ##\mathcal{H}_{1}## and ##\mathcal{H}_{2}##, such that their tensor product ##\mathcal{H}_{1}\otimes\mathcal{H}_{2}## yields a two-particle Hilbert space in which the state vectors are defined as $$\lvert\psi ,\phi\rangle...

From my humble (physicist) mathematics training, I have a vague notion of what a Hilbert space actually is mathematically, i.e. an inner product space that is complete, with completeness in this sense heuristically meaning that all possible sequences of elements within this space have a...