Qm Definition and 1000 Threads

Homework Statement Hi, am having difficulty with the Linear algebra in QM. We have been given a problem set and one of the questions am struggling with is as follows: Consider the space of all linear functions ##f(x) = ax + b## (x real) defined over the range ## -1 < x < 1 ##, with the scalar...

Apparently, there are two different routes to get to quantum field theory from single-particle quantum mechanics: (I'm going to use nonrelativistic quantum mechanics for this discussion. I think the same issues apply in relativistic quantum mechanics.) Route 1: Many-particle quantum mechanics...

Homework Statement [/B] The problem on where the photon will hit a screen, after passing through a single horizontal slit. I know the wavelength, slit width, magnitude of momentum of incoming photon (calculated), and distance between screen and slit. Homework Equations I just don't...

What are the mathematical relationships (if any) between the particles as described by Quantum Mechanics and the particles described by Quantum Field Theory? A specific question related to the general question above arose in post #14 of the thread: How can a particle be a combination of other...

Suppose that a static electric field E is applied on a conductive crystal. Then, how quantum mechanics describes the electron movements in the crystal? I have been trying to find an explanation, but have not found any. As I understand it, we could treat the E field as a time-dependent...

Does energy conservation law still hold if the system contact with varying source of energy? Because in QM the Hamintonian of the system always commune with itself,so the conservation law still correct.But if it is,where is the exchange energy between the system and the enviroment?

1. Homework Statement Homework Equations Here we have to express ##\psi(\theta,\phi)## in terms of spherical harmonics ##Y_{lm}## to find the angular momentum. If ##\psi(\theta,\phi) = i \sqrt{\frac{3}{4\pi}} \sin{\theta} \sin{\phi} ##, it can be written as: $$ \frac{i}{\sqrt{2}} (Y_{1,1}-...

Homework Statement Hi, in this book " [Nouredine_Zettili]_Quantum_Mechanics_Concepts ", Eq. (9.133) Homework Equations I don't know how the second line had come from the first line:The Attempt at a SolutionI got only two terms such that: $$ < \psi_0| H | \psi_0 > = A^2...

Hi all! Been a while since I was on PF and I greatly regret it. Forgot how great the community was. Anyways on to my point. I'm going into my second ywar of post secondary and planning to major in physics, and have the eventual goal of understanding both General relativity, and Quantum...

Hi everyone, according to some texts I ve read, there is not a clear definition for a quantum mechanical theory involving relativity. The most similar approach is that of Klein Gordon and Dirac equations, but there is not an analogy Schrodinger equation when we use relativity in QM. Can anyone...

Hi all, can anybody help me to find literature that takes the reader on a step-by-step path from non-relativistic quantum theory to relativistic quantum theory? I imagine something like that: it starts with a single harmonic oscillator, analyzes the non-harmonic oscillator (does the...

Does anyone know of QM notes (or a review article) that covers entanglement, the measurement problem, Bell inequalities, decoherence, or the delayed choice experiment (or the more recent mesoscopic experiments). So to speak the more modern and the exciting aspects of QM. I think closest to that...

I want to know what actually happens when light meets a surface like water or wood. Quantum mechanics says that objects are neither "transparent" nor "opaque". Rather a system as a whole can accept "energy packets" in certain ranges of energy and has no states available to accept other ranges...

Hi there PFers I'm looking into a variety of areas of research in electrical engineering at US universities. For instance, looking at the University of Texas page, there's a research specialty in EE called "plasma/quantum devices and optics." Now, this looks very interesting to me. I was...

Is there a bridge from QM to Crook's Fluctuation Theorem and/or the Jarzynski Equality? More ambiguously, but maybe more directly, Is there thought to be a relationship between the QM-entanglement/decoherence/interference, and the SLOT? I am worried I may be missing a discussion of this, due...

Just curious, but has this theory been completely disproven? Is it possible to even debate that this is the case? It seems to me that some of the founders of QM such as Heisenberg, Pauli, and even Max Planck toyed with this idea and considered it a possibility. Why is it not any more? I don't...

Homework Statement V(x) = -V ( if x > 0 ) 0 ( if x <= 0) ( V is positive constant) the transmission coefficient is not simply F2 / A2 ( with A the incident amplitude and F the transmitted amplitude ), because the transmitted wave travels at a different speed. Calculate...

Hello,I'm new here and this is my first post. I am a freshman electronics and communication engineering student.I didn't study any quantum mechanics or solid state physics before(not in high school). But for my first year course i need to study solid state physics.The books we are suggested to...

According to Maxwell's Equations, the classical vacuum permittivity and permeability have a very important role: They determine the speed of light. But it seems like these two important concepts are not as precisely defined in the quantum world. Are there rigorous analogs of these two...

I have a problem with the derivation of the the form of QM starting from the Lie algebra of the Galilei Group like the one given in Ballentine's cap 3. My Issue is that the procedure is shown almost as unavoidable, And my feeling is that there have to be more postulates that I'm not seeing...

Mathematically, a state in QM is a ray on the Hilbert space. But: 1) How would you define "state" from a physical point of view? I know a lot of examples but not a general definition. 2) Given a specific quantum system, to find all the states and so the Hilbert space, all I have to do is to...

The QM degeneracy pressure puts up a fight but the immensity of the star wins out. Why is this? Is the Pauli Exclusion Principle really a principle? Why does it surrender in this case?

Hi, I'm going to have a long graduate-level course on many-body quantum mechanics next fall and I'm already trying to prepare for it. I have the lecture notes that were used in the same course two years ago, but they are hand-written and a bit tedious to read. Can anyone suggest a good textbook...

Homework Statement Consider two spins, L and R, in a magnetic field along the z-axis, i.e. B = (0, 0, B) . The magnetic moments of the two spins are coupled to each other so that the total Hamiltonian reads H = g\mu_B\mathbf{B}\cdot(\mathbf{S}_L + \mathbf{S}_R) + J \mathbf{S}_L\cdot...

Homework Statement Using J^2 \mid j,m_z \rangle = h^2 j(j+1) \mid j,m_z \rangle J_z \mid j,m_z \rangle = hm_z \mid j,m_z \rangle Derive that : \langle j,m_z \mid J_-J_+ \mid j,m_z \rangle = h^2[ j(j+1) - m_z(m_z+1)] Homework Equations J_- = J_x - iJ_y J_+ = J_x + iJ_y The...

Hi I was trying the gram schmidt process on example 1.3.2 page 43 as shown below u1=(3,0,0), u2=(0,1,2), u3=(0,2,5)v1=u1=(3,0,0) v2=u2-proj_(w1) u2=(0,1,2)-((<0,1,2><3,0,0>)/9)(3,0,0) However the top line inner product gives 0...

I really like the book, its the first physics textbook that I liked actually. But I've found a minor error. On page 8 (chapter 1 The Wave Function) it says that if you sum deviations from average of a random variable you'd get zero because " Δj is as often negative as positive", here's the...

Hi Folks, How do we arrive at equation 1.8.7 page 33. We have ##<i|\Omega-\omega I|V>=0##, given ##I=\Sigma_{j=1}|i><i|## we can write ##<i|\Omega-\omega \Sigma_{j=1}|i><i||V>=0## not sure how to proceed from here...

I'm picturing a comoving particle, meaning at rest with respect to CMB? Does expansion affect the probability density, density current? I can't see how it wouldn't? But then it seems like there would have to be a uniform negative probability density current everywhere.

Let me define the question better. For my purposes I'm saying a person "understand quantum mechanics" when they have what it takes to write a basic graduate level QM textbook. Maybe I'm setting the bar too high, but I'm a first-year physics grad student who can get good grades in QM classes...

I'm interested in the derivation of relativistic Boltzmann equation from entropy after reading Scott Dodelson's wonderful cosmology book. Does anyone know of any good readings for this? The usual way of doing things in classical mechanics is to assume \frac{dN}{dt}= 0 and go from there; but...

I want to learn QM but in a way that i can learn both the deep mathematics, the physical intuition behind QM and the intuition behind the maths behind the QM(not many books have this). Note that this is my first attempt to learn QM and i will be watching some video lectures online,so i won't be...

Hello,i am just starting to learn Quantum Mechanics in the university at an underdrad level. I know there are a lot of great introductory books out there but i just saw that Landau's book on non-relativistic quantum mechanics has great reviews but upon seeing it,i was overwhelmed by the...

I've read several times in textbooks that in NR-QM you can measure with exact precision the position of a particle if you don't care at all for the momentum (because the uncertainty of the momentum will be infinite), it always seemed reasonable enough for me but now that I think about it, it...

In QM, time is reversible.. is there a setup where you can couple the system or interface it to classical apparatus such that you can access the time reversibility in qm and control it to reach the past and future (at least of the quantum system).. what would be this setup?

Hi, One of the main problems of the Rutherford model is the fact that the electrons are accelerated and hence should lose energy due to radiation. Bohr's model doesn't resolve this, it only postulates that the energy levels are quantized and energy can only be emitted or absorbed by jumping...

I did a search but couldn't find what I was looking for. I'm a physics student studying QM at the graduate level. I'm aware that "nobody truly understands QM" but I'd like to get as much insight and intuition as possible. Textbooks are good for learning to solve problems and learning the...

Bohm's deterministic theory was designed to be equivalent to standard QM, but what I'm not sure about is whether that includes Von Neumann's rules. Von Neumann's rules for the evolution of the wave function are roughly described by: Between measurements, the wave function evolves according to...

I was always a bit puzzled by the Heisenberg picture (not mathematically, I'm fine with that, but conceptually) - if a "state" describes a system, how can it not be time-dependent, if the system changes? I just found an alternative way of looking at it which seems to make sense to me, but I'm...

I'm trying to decide between Dirac, Shankar, Mandl, Griffiths, Gasiorowicz, and Sakurai for an undergrad QM course. It is the first "proper" quantum course after a basic introduction in the modern physics class, but apparently it is particularly mathematically challenging, so I'm looking for a...

Does something in QM suggests that "everything is happening, here/now at once? Is there any evidence to prove it? (quantum reality) I saw a video about it on the internet, I will not post the source, because I think it is pseudoscience, but he confirmed that QM proves it..lol Please, I don't...

See the picture below for details. I have included my solution thus far, but it doesn't feel right and I'm just wondering what I am missing. Any assistance would be greatly appreciated, cheers.

Homework Statement I'm asked to calculate the reflected and transmitted part of the wavefunction, in fact, this is the first time i encounter this so i need your assistance. Homework Equations Time independant schrodinger equation + continuity condition The Attempt at a Solution See the...

I'm an EE major doing a minor in physics. I have to take a standard intermediate electromagnetism course from the engineering department (which is just a more applied version of the physics department course). To get my minor, I was thinking about getting permission to use this course as a...

What math should a person know to THOROUGHLY understand everything in this textbook(Introduction to Quantum Mechanics by David Griffiths)? (For refrence) cal2 cal3 diffeq1(ode) diffeq2(pde) linealg vectorcalc realanal1 realanal2 Please list all you think are necessary. Thanks

Hello over the summer I would like to study quantum field theory. I took two semesters of undergraduate quantum mechanics using Griffith's textbook. We covered the entire book in those two semesters. I also know my special relativity pretty well. Is that enough to self study quantum field theory...

I have impression that physicists consider QM laws as fundamental, meaning that there should be a way how QM mathematical form is realized in reality. On the other hand QM laws could be effective laws resulting from some process of evolution. In that case it should be possible to characterize...

Apologies if this should be in homework section but I thought it best suited here. Been revising past papers but with no solutions. the following questions all require just a true or false answer. Any help or confirmation of my answers would be appreciated. 1 - every N x N matrix has N...

Say you take an open circuited loop (not connected back to itself) and measure its voltage relative to some external reference point. Then you start rotating this loop in a magnetic field. Depending on the power of your motor, the loop will continue to spin for a finite amount of time. After...

Hello science buddies, This is my first post in this forum. Ok let me get to the point directly, currently I self-study graduate level quantum theory and the main book I'm using is Sakurai's. But I think for self studying it's better to also have a look at lecture notes, first because it's much...