Qm Definition and 1000 Threads

Is there some fuzzy area between the macroscopic and atomic worlds where gravity "still sort of works," or is it a dramatic cut off? I never understood this whole idea that it suddenly stops making sense at the quantum level. Does it start making progressively more sense as you increase the scale?

I find the fundamental postulates of QM very ad-hoc and strange. Compare them to the fundamental postulates of special relativity, special relativity naturally arises out of classical electromagnetism and the equivalence of all inertial frames, while QM seems to come out of nowhere.

QM--- matrix exponentiation Homework Statement \ How do you go about exponentiating a 3*3 matrix? for example if you have <θ,∅|exp(-i*∅*Ly/h)|l,m> Homework Equations I know how to exponentiate a two cross two diagonalized matrix. you just exponentiate the diagonal terms...

Homework Statement Hi guys, I don't really know how to solve the first part of a problem which goes like this: Consider a 1 dimensional harmonic oscillator of mass m, Hooke's constant k and angular frequency ##\omega = \sqrt{\frac{k}{m} }##. Remembering the classical solutions, solve the...

I've had a proof based linear algebra course as a freshman, where I learned that the spectrum of an operator was the set of the eigenvalues of that operator. Now in quantum mechanics I learned that this isn't true and that the spectrum of an operator can contain infinitely more numbers...

Homework Statement This problem is about the 1-dimensional harmonic oscillator. The normalized energy levels are labeled |n>, n=0,1,2... Two operators are given by \widehat{A} = \alpha (\widehat{a}++\widehat{a}-) \widehat{B} = i\beta (\widehat{a}+2+\widehat{a}-2) where \alpha and...

In class, my teacher was motivating Schrodinger's Equation, but there is one step that I do not understand or even have intuition for. I'll give the argument leading up to the step I do not understand for context. Let \hat{U}(t) be the operator that gives the wave function after time t, given...

Hi, Can anyone explain to me why the wave functions in QM must to be complex, other than to make it work when inserted into the Schrodinger equation?

Homework Statement Hi guys, I'm stuck at some step in a QM exercise. Here it is: Consider a free particle of mass m that moves along the x-axis (1 dimensional). Show that ##\frac{dA}{dt}=\frac{2 \hbar ^2}{m^2}\int \frac{\partial \psi}{\partial x} \frac{\partial \psi ^*}{\partial...

well i am a starter in QM, i have 2 big doubts ! let me first tell what i understood , there is phsi which defines a state of a system, phsi times x is a position operator and phsi 's derivative of x multiplied by i h is its momentum operator ... well then i operator these in phsi and what do...

Homework Statement Electrons with energies of 0.201 eV are incident on a barrier 2.386 eV high and 0.383 nm wide. Find the probability for these electrons to penetrate the barrier. Homework Equations Note: h = h-bar k=Sqrt[2*m (V - E)]/h T = (1 + (V^2 (Sinh[k*L]^2))/(4*R (V -...

In classical mechanics is defined potential and kinetical energy for particular particle. For example, in case of free fall potential energy of the particle is ##mgh## and kinetic energy is ##\frac{m\upsilon^2}{2}##. In QM there isn't potential of the particle, but potential of part of the...

Homework Statement Hi guys, I've an integral that poped up in QM, it should be different from 0 (else the particle's position is known with 100% certainty while it should not with the wave function I was given). However I get 0 and I don't see where my mistake(s) is/are. ##<(x-a)^2>=\int...

Homework Statement Suppose that we have a source of particles (e.g. photons) S, then three slits labelled 1,2 and 3, followed by a screen. For a particle that has passed through slit i, where i=1,2,3, let ψi(x) be the amplitude for the particle arriving at a position x units along the...

Someone asked me which math topics to study in order to learn quantum information theory. I thought it was a good question, so here's my answer. Warning: this is off the top of my head, so it probably needs additions and/or corrections. Most of this advice applies to anyone doing quantum...

Homework Statement For the n = 1 harmonic oscillator wave function, find the probability p that, in an experiment which measures position, the particle will be found within a distance d = (mk)-1/4√ħ/2 of the origin. (Hint: Assume that the value of the integral α = ∫01/2 x2e-x2/2 dx is known...

I am new to this area, so pardon me if the below question might seem... 1. What area/subject/sub-topic of physics deals with attempts at bridging GR and QM? 2. What does it say? in layman language 3. What is a quantum field? 4. is there any area of QM where some credible mathematical...

In problem of infinite potential well particle can't be in a region where ##V=\infty##. How we know that in case of finite potential well that particle is in the region where ##V>E##. How we know what is energy of the particle in moment when we localize it in the region with potential ##V##...

Coordinate representation ##\psi=\psi(x)## Momentum representation ##\psi=\psi(p)## Fourier transform \psi(p)=\frac{1}{\sqrt{2\pi\hbar}}\int^{\infty}_{-\infty}\psi(x)e^{-\frac{ipx}{\hbar}}dx I'm confused with this ##\hbar##? Why not...

Greetings all. I'm a new poster here but have spent some time on philosophy forums previously. I subscribe to New Scientist and try and stay reasonably current with science, on the popular level at least. This week they have had a feature about physical cosmologies and 'theories of...

A long time ago, maybe 6 months, I saw an annual survey of which QM interpretation people adhered to and there was a list of maybe 10 different interpretations. I tried to find it again but couldn't. I used the advanced search tool for about 15 minutes but couldn't find anything. Does anyone...

I was wondering whether Oppenheimer's legendary QM lecture notes still exist and can be found somewhere. I only found the content of theses lectures at http://bancroft.berkeley.edu/Exhibits/physics/learning03.html I assume Bohm's book ``Quantum Theory" from 1951 must contain some of the...

I'm kind of rambling here since I'm not sure how to formulate what I'm trying to say. Is there an interpretation of quantum mechanics that uses topos theory? As in is there a way to fix some of the logical paradoxes of QM interpretations, by using a many valued logic system?

Homework Statement Show that the Hamiltonian H = (p^2/2m)+V commutes with all three components of L, provided that V depends only on r.Homework Equations In previous parts of the problem, I've worked out the following relations: [L_z,x] = i\hbar y, \quad [L_z,y] = -i\hbar x, \quad [L_z, z] =...

It is ok for physics to distinguish between me and a rock out somewhere on the surface of Mars ? Who am I but a bag of chemicals ? Why would my action of observing be of any significance ? Why should the moon be "paged-in"/from-into-existence when I "observe" it and other times it is allowed...

I get the feeling that when we say that electrons sometimes are particles or a wave depending on whether or not we measure it that what we mean by wave is not what first comes to people's mind. When we measure the electron it becomes a particle, if not then it is a wave. When I think of wave I...

I am trying to understand how QM theory (wave-functions) are applied to Interference pattern calculations for unequal slits for a single particle double slit experiment case 1: both slits are equidistant from the "center", however one slit is bigger and the ratio of the width between the slits...

Hello, I am looking for more information on the axiomatic treatment of physics. I have found some articles concerning the axioms of quantum mechanics, i.e. the Dirac-Von Neumann axioms. However, I am having a hard time finding anything on the classical version of these axioms. In these...

Homework Statement What is the probability that an electron in the ground state of hydrogen will be found inside the nucleus? a) First calculate the exact answer, assuming the wave function \psi(r,\theta,\phi) = \frac{1}{\sqrt{\pi a^3}} e^{-r/a} is correct all the way down to r=0. Let b be the...

In molecular orbital theory, only the electrons are considered and from that we draw conclusions about molecular shape and such. I was thinking just now, what about the nuclei? If we apply QM to the nuclei as well, wouldn't that mean that we can't know where the atoms are? or is the...

Homework Statement Consider a quantum system with a countable number of basic states \left|n\right\rangle. Calculate the decomposition into a basis of coherent states \left|λ \right\rangle all obeying \hat{a} \left|λ \right\rangle = λ \left|λ \right\rangle Homework Equations \hat{a}...

Homework Statement There are two ways to write the momentum operator, p = (-i hbar d/dx) and p = (hbar / i)d/dx. How do you go from one to the other? Homework Equations The two I gave above. The Attempt at a Solution I tried to see if -ih = h/i by squaring both sides, but one came out...

Hi everybody, i didn't wanted to create two separate threads so merged them into one. i got confused watching Brian Green explaining QM on one of his shows. He compared distribution in double slit experiments with throwing a ball on a roulette. He said that casino doesn't have to know...

It is well known that unbounded operators play a crucial role in the mathematical formulation of quantum mechanics. In some sense, unbounded operators are inevitable. Indeed, we can prove that if A and B are self-adjoint operators such that [A,B]=ih, then A and B can never both be bounded. My...

According to the Copenhagen Interpretation, and considering Young's double slit experiment: Is what interferes the mathematical wave function flowing out the two slits but the electron itself takes a well defined path? Anyhow, I need a clearer idea about the position definition or...

Homework Statement How to prove that for any representation of the spin, the state e^{-i{\pi}J_x/\hbar}|j,m\rangle is proportional to |j,-m\rangle The exponential term is the rotation operator where J_x is the x-component of the total angular momentum operator, and |j,m\rangle is an...

Hi I was day dreaming the other day when I realized how incomplete and vague the fundamental postulates of QM are, I mean what counts as an observation? For example simply being in the presence of a charged particle can be an observation, since (using a point particle for the sake of argument)...

Is there some fundamental fact of the universe (Quantum Mechanics) that prevents us from removing noise (without having to compare the entangled particles)? In the quantum eraser experiments: To get ("un-embed") the interference pattern i.e. to separate the entangled particles from the...

Homework Statement Basically I need to produce a state for a spin-1/2 particle such that the expectation value of <Jz> = 0 where <Jz> is for a spin-1 particle. Homework Equations Jz = (1 0 0, 0 0 0, 0 0 -1) <--[3x3] matrix The Attempt at a Solution I don't quite understand how to do this...

In special relativity an event E is mapped to coordinates (x,t) in one inertial frame, and to coordinates (x',t') in another, and SR provides the relation between (x,t) and (x',t'). What is the empirical content of this theory (e.g. how would you operationally test it)? Since there are two...

Greetings everyone, This is my first post although I have referenced this site numerous times. It's a great resource, so many thanks to the admin and participants. A little background: I am in my junior year of a physics/mathematics double major at an unremarkable state university. The...

The situation is messy so I'll avoid details. I absolutely must do one module this February that is listed as 'level 3' at the Open University without formally taking the prerequisites. I have to teach myself the required mathematics, in two months, to give myself a decent chance of passing. If...

Hi I have a question on how to work with quantization axis. The setup I am looking at is a single two-level atom placed at the origin (0, 0, 0), which is not perturbed by any magnetic field. I now send in a laser resonant with the transition of the atom. With a right-handed coordinate...

I am a third year physics major and am studying quantum mechanics using Griffiths' textbook. I can do most of the problems with one star or no stars with relatively little effort, but a lot of the problems with three stars I find very difficult and I cannot do them at all. For the average...

Homework Statement A particle in the infinite square well has its initial wave function an even mixture of the first two stationary states: \Psi(x,0) = A\left[ \psi_1(x) + \psi_2(x) \right] Normalize \Psi(x,0). Exploit the orthonormality of \psi_1 and \psi_2 Homework Equations \psi_n(x) =...

I'm beginning to study QM, and as I understand all the information we can get out of system with 1 particle is the probability distribution function (which has position and time as variables). By knowing the wave function it's possible to know the probability distribution function, but that's an...

Why all operators in QM have a Hermitian Matrices ?

I'm actually quite scared of asking this due to my very basic knowledge regarding Quantum Mechanics. Actually, this is my first hiccup: is there a difference between Quantum Physics and Quantum Mechanics? I always thought one was the theoretical investigation and the other the application but...

Classically, a direct measurement of velocity requires two measurements - position at time t1 and position at time t2. In QM such a measurement is not meaningful, since measuring position at time t1 would necessarily affect the particle (i.e. cause it to collapse to some position eigenstate)...

Hi all, I'm taking graduate level QM I and trying to wrap my head around the notion of gauge symmetry. For some reason I've struggled with this concept more than others. I don't really have a specific question; I'm more looking to see if someone has a succinct explanation of the relevant...