In quantum mechanics Definition and 251 Threads

I have several questions about symmetry in quantum mechanics. It is often said that the degeneracy is the dimension of irreducible representation. I can understand that if the Hamiltonian has a symmetric group G, then the state space with the same energy eigenvalue will carry a...

In proving that for the norm to be preserved, U must be unitary. I ran across this: Re(λ<ø|ψ>)=Re(λ<Uø|Uψ>) if λ=i, it says that then it follows that Im(<ø|ψ>)=Im(<Uø|Uψ>), how's this? I know that Re(iz)=-Im(z) in complex, but here the inner product <ø|ψ> is not z, or is it? If you...

hi, from study of quantum mechanics i infer that wavefunction is a dummy function on which you apply required operator like momentum operator, energy operator etc., and their eigenvalues gives you the value of observable? i want to ask my interpretation of wavefunction is correct? or not?. thanks

I understand this is probably a very stupid question to some of the people on here, but none the less i would still like to know. It hasn't been explained very well to me. I have a vague understanding that it is a number that you collect for each possible path? Please correct/elaborate on this...

Could someone explain what this crazy new discovery means? Is it the rosetta stone of QM?

Which contemporary physicists in theoretical or experimental physics do you think should be included in the group of the Top 10? You do not have to rank them within the group. I just want to identify leading physicists, their research groups and geographical hot areas for QM, like the...

Over the past few weeks I have been attempting to research opportunities for specializing in quantum mechanics/quantum field theory or a related field such as particle physics. I was wondering what the best academic path would be for this field of study and what my chances are of finding a...

Why velocity in quantum mechanics is meaningless while we can always put v=p/m where p is momentum?

Hello, I'm doing an undergraduate introductory course in quantum mechanics, and I'm having a hard time understanding the interpretation. I've recently learned about the famous "Particle in a box" problem, in which we solve the time-independent schrodinger wave equation to get the energy...

hello,ereryone.I am a senior in china... Someone asked me this question,and suddlenly i have no idea. Please,give me some help. thank!

has anybody read this book?? DO you think solution to questions of this book are good ??

There is a statement in the Landau and Lifgarbagez volume on quantum mechanics that has had me puzzled for weeks now. They say (bottom of pg. 23): "If the electron was in the state psi_n [an eigenstate of f], then a measurement of the quantity f carred out on it leads with certainty to the...

because Schrodinger equation is a linear differential equation. How do we show that Schrodinger equation is a linear differential equation?

in quantum mechanics we have something called hilbert space. What does the dimensions of this space represent for that system? also is ψ(x) same as |ψ> in the dirac notation?

It follows from the Expectation value postulate that an observable A, associated with the operator A^, can be precisely measured only if the wave function ψ of the system is an eigenfunction of A^ . Accordingly, the position and momentum of a particle can never be precisely measured because...

Homework Statement Homework Equations i think the most relevant equations would be some commutator algebra theorems i do not know of ! The Attempt at a Solution

Homework Statement In quantum mechanics, what objects are the members of the vector space V? Give an example for the case of quantum mechanics of a member of the adjoint space V' and explain how members of V' enable us to predict the outcomes of experiments. Homework Equations The Attempt...

Unfortunately, I can't find the thread (if someone finds it, please let me know, and I'll merge this post onto that thread), but someone asked why it is that in quantum mechanics, if you have an observable $B$, that the expectation value (average value) $\langle B \rangle$ is given by $$\langle...

Ok so I'm currently revising my quantum theory course from this year and I've reached the section on the postulates for measurements in quantum mechanics. The one I'm having trouble with is "The only result of a precise measurement of some observable A is one of the eigenvalues of the...

I am doing some reading on Quantum Mechanics, and I do not understand this concept. Here is an excerpt from "The Universe and the Atom" by Don Lichtenberg. Sorry for the bad formatting. I don't understand why we can't answer which slit the particle when through. What else could it have gone...

Hello It is question of specifying mathematical definitions which are cummunes in several theories. In classical physics, in special relativity, in quantum theories (wave functions and state vectors) and in general relativity, we can assert : (a) The universe U is a topological space...

Major anxiety! I'm in undergrad honors quantum mechanics II. I got an A in honors quantum mechanics I. It was darn hard but I did it. My problem is that I feel like all I'm doing is keeping up, chapter to chapter, topic to topic, without anything really sticking. I feel like a total...

If you have an operator a represented in some basis l1>, l2> you find its matrix elements by doing Aij = <ilAlj> But more oftenly you are interested in the expectation value of A. So you take: <ψlAlψ>. My teacher tends to call these numbers matrix elements too. But which matrix element...

As I understand it wavefuctions of individual particles are incomplete descriptions of a system because ultimately a wavefunction describes a system and cannot be reduced to individual particles (which would exclude things like entanglement). So the only way to have a good idea how a system...

Homework Statement What is the correct interpretation of < \frac{\partial {A}}{\partial t} >, where A is an operator?Homework Equations for a wave function \phi and operator A, <A> = \int_{V}\phi^{*}(A\phi)dVThe Attempt at a Solution I thought it could mean < \frac{\partial {A}}{\partial t}...

Just an idea: is there an index theorem for an n-dimensional Hamiltonian H = -\triangle^{(n)} + V(x) which "counts" the bound states (H - E) \,u_E(x) = 0 i.e. eigenfunctions and eigenvalues in the discrete spectrum of H?

What are the specific properties of time in quantum mechanics? One thing I have often wondered is, Does time exist in multiple quantum states until it is measured? IE. is time an unknown variable until the act of measurement is performed by some kind of measuring device? (a sun-dial, a...

im finally writing my conclusion for my Extended Essay. The extended essay (EE) is a mandatory core component of the IB Diploma Programme. It is a research paper of up to 4,000 words giving students an opportunity to conduct independent research or investigation on a topic that interests...

Homework Statement Given a system initially in a state $$| \psi \rangle = \frac{1}{\sqrt{6}} \left(|1\rangle + 2 |2\rangle + |3\rangle \right)$$ where ##{|n\rangle}_{n=1}^{8} ##form an ON basis. If we perform a measurement of an observable corresponding to an operator...

is it pauli or schrodinger? is there any original reference?

Hi. I have read some QM and am trying to use it to understand why the noble gas configuration is the most desirable for an atom. It is my understanding that an anti-symmetric spatial wavefunction has a lower energy, since the electrons tend to be further apart. This means that the atom will...

A particle in the ground state of a potential well can only gain energy by making a transition to one of the higher allowed energy levels. Let's consider this well to be a 1 dimensional infinite potential well with the electron bouncing between the walls of the well with certain discrete...

Hi, guys, As a beginner, I have some problems to understand QM. Thanks a lot in advance for your response ! 1. According to QM interpretation, the measured particles, they become spike, do they have chances to back normal status (the status before becoming spikes)? If yes, how? if no...

In the book Introduction to Quantum Optics: From the Semi-classical Approach to Quantized Light by Grynberg, Aspect and Fabre I came across the following statement on page 385: "By the end of the nineteenth century, classical electromagnetism,..., provided a wave description of almost all...

in Quantum Mechanics Problem it must be ∫ψ*d3ψ\dx3 dx =∫d2ψ\dx2 dx how ? ? i think it will be by inGration by parts i need steps

Homework Statement Define measurement in the Copenhagen interpretation of quantum mechanics. Homework Equations The Attempt at a Solution In the Copenhagen interpretation of quantum mechanics, measurement changes the state of a wavefunction, that is, it collapses the wavefunction...

There are tons of interpretations of quantum mechanics, but I'm unaware of any that are 'classical' as in being local, having realism and determinism. There is Bells famous work proving that that can't be true for certain aspects of quantum mechanics, but why aren't there any classical...

What does "state" mean in quantum mechanics? I'm currently self learning quantum mechanics from Griffith's book. I'm in the first chapter and he's using phrases like "a particle in state Ψ", but he doesn't explain what it means by "state". Can someone please enlighten me?

What is the opposite of "realism" in quantum mechanics? I have been spending an awful lot of time reading about the philosophy of science where the opposite of "realism", insofar as "realism" constitutes a category coherent enough to be meaningfully negated, is "anti-realism". Is this true as...

Hey, I'm a second year physics undergrad and I'm interested in doing research in quantum Physics after I graduate. I'm just wondering what programming language I should be focusing on to enable me to carry out such research I've done introductory courses for Mathematica, Matlab and C++ and so...

Homework Statement In an infinite potential hole, the ground state is described by the wavefunction ψ=A*sin(\frac{πx}{a}). Does the ground state have a definite momentum? If not, then what are the values of momentum in ground state? Homework Equations Wavefunction ψ=A*sin(\frac{πx}{a})...

When we setup the Schrodinger equation for the hydrogen atom we use the classical electric potential. It seems that we would need a new potential instead of mixing QM and classical. Is this just a very good approximation or is there something subtle.

What should we use to express free particle in Quantum Mechanics? Wave packet or plane wave? Can free particle be localized in Quantum Mechanics?

THe EQUATIONS IN THIS POST HAVE NOT GONE THROUGH SO WILL TRY TO FIX THIS AND RE SUBMIT ASAP (I used mathType?) Now attached the post as a word file to fix the above. I’m playing around with possibilities and my own ideas about “the measurement problem” and have a query about the validity...

In <Engineering Electromagnetics> written by W.H.Hayt and J.A.Buck( 6th edition,McGraw-Hill,p372), the phase velocity vp of electromagnetic waves in copper at 60Hz (commercial electric power) is 3.2m/s. Substituting the value into vpv = c2 of de Broglie theory, v=108c should be much faster...

Hi there, The average expected result for particles with 1/2 probability going through slit 1 and 1/2 probabiltiy going through 2, for a large number of particles (N) is exactly that: 1/2 slit 1, 1/2 slit 2. We send the large number of particles through and find that roughly half go...

Homework Statement why we do use commutation? what is physical difference between commutators and Poisson Brackets? Homework Equations The Attempt at a Solution

Hi all, In our assignment, we were given this question: [PLAIN]http://img685.imageshack.us/img685/4854/prob213.png I know that for (a), the answer is the first energy eigenstate since the measured energy corresponds to it. I'm not sure about the situation in (b), though. Does...

Hi all, In my class we were given an assignment from Introduction to Quantum Mechanics by David Griffiths. The question is in Chapter 3, problem 3.34. http://img41.imageshack.us/img41/7899/prob334.png (The system has a harmonic oscillator potential.) Right now I'm stuck with...