In quantum mechanics Definition and 251 Threads

Homework Statement This is problem 2.11 from Griffith's QM textbook under the harmonic oscillator section. Show that the lowering operator cannot generate a state of infinite norm, ie, \int | a_{-} \psi |^2 < \infty Homework Equations This isn't so hard, except that I consistently get the...

Homework Statement Find the maximum accuracy that can be found to a proton's position without changing it's (not-realativistic) kinetic energy by more that 1 keV I think this involves Heisenberg's uncertainty principle \Delta x\Delta p=hbar/2 but I am not sure at all. Now to find the...

Hi everyone. I am now learning the perturbation theory in QM. and I have encountered something that puzzles me. from http://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics ) says, "...Since the overall phase is not determined in quantum mechanics, without loss of...

In CM, we have a prescription for measuring momentum. Velocity is defined, and we can measure it, and we can find out the momentum. Now, does quantum mechanics have the same prescription for measuring momentum (for a single free particle at least) ? I mean, for a single free particle, can we...

Can someone please tell me what the integrand in the below equation mean? 1 = \langle \psi | \psi \rangle = \int_{-\infty}^{\infty} d \langle \psi |E_\lambda \psi \rangle where, E_\lambda is an increasing (and absolutely continuous) function of projection operators such that...

Homework Statement Write all orthogonal matrices in the form e^{i\phi \frac{\hat{n}\bullet\vec{L}}{\hbar}}. Homework Equations The Attempt at a Solution I couldn't understand the question. An orthogonal matrix R satisfies R^{T}R = RR^{T} = I and rotation matrices in 3 dimensions...

what does the momentum in de broglie wavelength signify? i mean how do u defien it...we can define the expectation in momentum but how do we define momentum for "quantum mechanincal" particles

i.e things happen for no cause. Thx

Homework Statement I recently tried to do the following integral: an = ∫√(2/a) sin(n∏x/a) cosh(x) dx x=0 to x=a Homework Equations an = ∫√(2/a) sin(βx) cosh(x) dx β = n∏/a sin(βx) = ½i(eiβx – e-iβx) cosh(x) = ½(ex + e-x) The Attempt at a Solution an = ¼ i √(2/a)∫ (eiβx – e-iβx)...

I am trying to calculate the variance of the position of a particle in a one dimensional box (quantum mechanics). I have a wavefunction, and I know the probablilty density is the integral of (the wavefunction squared) with respect to x. Can you please tell me how this wavefunction could be...

Hi everyone. This is kind of a geometry/quantum mechanics question (hope this is the right place to post this). So, in quantum mechanics we consider operators that reside in an infinite dimensional Hilbert space (to speak rather informally). We even have the cool commutator relation, which is...

We know that the Hilbert space of wavefunctions can be spanned by the |x> basis which is a non-countable set of infinite basis kets. Now consider the case of a particle in a box. We say that the space can be spanned by the energy eigenkets of the hamiltonian (each eigenket corresponds to an...

In classical mechanics the Lagrangian depends only on time, position, and velocity. It is not allowed to depend on any higher order derivatives of position. Does this principle remain true for Lagrangians in non-relativistic quantum mechanics? What about relativistic quantum field theory...

i was reading about the mathematical formulation of quantum mechanics and how a system at any given time is described by a vector represented by an infinite number of spatial complex number coordinates. does this infinite-dimensional state space have any physical significance or is it just a...

I read some derivations of current density from the quantum equations of motion (like Scrödinger's and Klein-Gordon's). They derive an equation with the same form as continuity equation: div(A)+dB/dt=0 Then they conclude that A=current density and B=density. However there are non-zero...

Why forces are modeled as virtual particles in quantum mechanics and how virtual particles can transmit force between two real particles?

hi all, I have a problem about rotation operator in QM. I must verify that (\hat{U}(R)f)(\textbf{x})=f(R^{-1}\textbf{x}) with: \hat{U}(R) = exp({\frac{-i\varphi\textbf{nL}}{\hbar}}) R rotation on versor n of angle \varphi I don't really know how to start, so please give me an advice!

How rare is it for a freshman in college to be taking quantum mechanics? I know a crazy freshman who is going to be taking it with me next quarter.

Can anyone explain to me what how is the act of observation defined in quantum mechanics? It is commonly said that the double slit experiment shows that if one simply observes the state of the electron as it passes through the slits, it effects the results. Many forms of observations are...

I am studying Quantummechanics, but I don't see how Fourriertransforms in quantum mechanics work I want to know how I can Fourrier Transform the Hydr. ground state, so the transform of \phi\left(r\right)=\left(\frac{1}{\pi a_{0}^3}\right)^\frac{1}{2} e^\left-(\frac{r}{a_{0}}\right)...

I have a question about bound states as they relate to a question on my homework... From what I can see, bound states in quantum mechanics are associated with energies that are discrete, not continuous. I don't really understand why... In my homework problem we are given a set of potential...

Is U(t)=exp(-iH/th) a Lie group? Is it an infinite dimensional Lie group? To what 'family' of Lie groups does it belong? thank you

I'm a newcomer here... so I introduce myself: I've just completed my BS in physics and joining M.Sc... I've interested to take specialisation in Quantum mechanics and will continue in theoretical physics in the future... I'm facing problems understanding the algebra of operators...

What for do we need operators in QM. Where is the complete state description of a quantum object?

Hi, For example, if I were to send |y> = 1/sqrt{2}( |H> + |V> ) photons into a polarizer with a 45 degre angle from horizontal, would the beam loose intensity? How can I calculate it on my own? EDIT: The picture below illustrate what is happening. I am changing the base from x-y to a...

Hi all, I'm new to his forum. I'm having trouble with the following question on central potentials. It's an exercise from (Bransden and Joachain, Introduction to quantum mechanics). Homework Statement Suppose V(r) is a central potential, expand around r=0 as V(r)=r^p(b_0+b_1r+\ldots). When...

The spin of an electron is described by a vector psi = column vector with two entries,psi up and psi down Give the general expressions for the probabilities to find Sz= +or- h/2 in a measurement of S^z where Sz=h/2(1 0) as a matrix ( 0 -1) ii)Give the general...

can anyone help?? in quantum mechanics commutator prove [L^x,L^y] = ihL^z given :L^x =(y^(pz)^-z^(py)^) :L^y =(z^(px)^-x^(pz)^) :L^z =(x^(py)^-y^(px)^) where ^ is just showing its operator prove comutator [L^x,L^y] = ihL^z I am swamped at every hurdle and can't seem to get my...

I'm a biology student, but I take some interest in physics and have read 2 of Stephen Hawking's divulgation books about modern physics and often stop to read something about it in wikipedia. Wich has revealed to obviously not be enough to understand some characteristics of Quantum Mechanics...

Homework Statement Within the framework of quantum mechanics, show that the following are Hermitian operators: a) p=-i\hbar\bigtriangledown b) L=-i\hbar r\times\bigtriangledown Hint: In Cartesian form L is a linear combination of noncommuting Hermitian operators. Homework Equations...

As part of an exam paper I've been using to revise with, I came across a question that simply says "What is parity?" Well I know vaguely what it is. Its to do with whether a wave is odd or even right? For example for cos and sin odd parity occurs because sin(-x) = -sin(x) and cos(-x) =...

My calculations always come out all right, but I still feel that I need help conceptualizing the potential well. 1.What does the width(or length) of the well represent? 2.What does the depth of the well represent? Sincerely appreciative, Yonderboy

The Hamiltonian is given: H=Aâ†â + B(â + â†) where â is annihilation operator and ↠is creation operator, and A and B are constants. How can I get the eigenenergy of this Hamiltonian? The given hint is "Use new operator b = câ + d, b† =c↠+ d (c and d are constants, too) But...

http://realityconditions.blogspot.com/2006/09/on-price-and-penrose-on-time-asymmetry_18.html" is a very interesting discussion of a proposal to allow backward causation in quantum mechanics. The basic idea is that the time asymmetry of QM ("collapse of the wave function") violates our...

First it asks a few questions about what if it were a classical particle approaching the barrier. Much of this I understand and am OK with. Then we start treating the particle as a quantum thing so its governed by the TI Schrodinger EQ. So, what it wants me to do which I am a bit unsure about...

Problem 1.17 in griffiths gives, at time t = 0, the state psi =A(a^2-x^2) for -a to a, and 0 otherwise. It asks then to find the expected value of momentum p at 0 and also the uncertainty in p. How do I do this? The only way momentum is defined is md<x>/dt, and since the state is only for time...

Hi, We recently solved the hydrogen atom and one of our homework problems asks us to replace the coloumb potential with a gravitational potential. I have the potential as being V(r) = -\frac{GMm}{r} Where M is the mass of the sun, m the mass of the earth. I have calculated the Bohr radius to...

CAn anybody guide me about what are the prospectus for jobs if one gets masters in quantume mechanics? pls om namah shivay

Hi, can anybody help me with this problem? I am currently study quantum mechanics and am confused with the BE staticstics. OK, say there are N Bosons in a system with two energy levels. The lower energy level is 0 and the upper level is E. The question is what is the average occupancy of the...

As I read in my quantum mechanics book the delta function is sometimes called the sampling function because it samples the value of the function at one point. \int {\delta (x - x')} f(x')dx' = f(x) But then I opened a quantum field book and I found equations like that: \phi (x) =...

What kind of math does QM use (beyond calculus, differential equations and linear algebra)?

When you calculate the probability of an electron being somewhere, eg in the case of orbitals, is the result in the form eg 1/2 or 50%, 1/4 or 25%, etc? Or is it of some other form? Thanks.

I am familiar with the normalization \int\left|\Psi\right|^{2}dx=1 Because we want to normalize the probability to 1. However if a state vector isn't in the x basis and is just a general vector in Hilbert space, we can take the normalization condition to be: <\Psi|\Psi>=1...

Does quantum mechanics allow an observer free choice of measurement?

Consider the wave function corresponding to a free particle in one dimension. Construct the probability density and graph it as a function of position. Is this wavefunction normalizable? Now, I think that the function should be Psi = C1*exp(ikx-iEt). Thus, the probability density should be...

I was just thinking how photons fit into QM, I've heard people speak of "photon wavefunctions". In particular I am wondering whether its bound by the Uncertainty priciple, I guess it can't be... since we know its exact velocity (i.e delta(x) = 0, at least in a 1-d case =P) how could we...

I've always though of particles in the following sense: If you do NOT measure/decohere a particle in some way, it exists ONLY as a probability wave--there is no "actual" number for each of its unknown quantity, just a probability of what it will be. There are no "hidden variables" that we...

Newton was separate from his clockwork universe; in the last century we have realized that we experimenters really subjectify the outcome of our experiment by attempting to exclude ourselves from it. Both quantum mechanics and cosmology involve an observer who participates by disturbing an...

As in quantum mechanics a photon can find itself at 2 different places at the same time, does time then exists at that level ?

Hi, I am a high school student, and I am planning on going into quantum computers as a profession. However I have failed so far to find any resources or teachers, organized in any fashion to help me to get a head start on the subject before I have to tackle it in college. I feel it is very...