Oscillator Definition and 1000 Threads

Homework Statement Consider a particle of mass m moving in a 3D potential V(\vec{r}) = 1/2m\omega^2z^2,~0<x<a,~0<y<a. V(\vec{r}) = \inf, elsewhere. 2. The attempt at a solution Given that I know the solutions already for a 1D harmonic oscillator and 1D infinite potential well I'm going to...

Why does in QM the electron does not fall toward the nucleus? After all, the only force between nucleus and electron is attractive. It seems that the electron can and does indeed fall toward the center in <simple harmonic oscillator>? My question is what's so different in these two systems...

A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along the rope in 10.0 s. What is the wavelength?

Homework Statement Trying to normalize the first excited state. I have, 1 = |A_1|^2(i\omega\sqrt{2m}) \int_{-\inf}^{\inf} x \exp(-m\omega x^2/2\hbar) How do I do the integral so I don't get zero since it's an odd funciton?

My question is pretty easy (i think). I have a wavefcn PSI defined at t=0. The PSI is a mix of several eigenstates. Let's say PHI(x,0)=C1phi1 + C2 phi3. Now C1 and C2 are given to me, so I am wondering is this wavefcn. already normalized, or do i have to normalize it despite definite C1 and C2...

Hi! Would anyone be able to point me toward a detailed explanation of determining the Hamiltonian of a polyatomic quantum oscillator? My current text does not explain the change of coordinates ("using normal coordinates or normal modes") in detail. All I can find is material on a diatomic...

Homework Statement Consider the anharmonic potential U(x)=cx2-gx3-fx4 and show that the approximate heat capacity of the classical unharmonic oscillator in one dimension is C=kb[1+(3f/2c2+15g2/8c3)kbT] Homework Equations U(x)=cx2-gx3-fx4 and heat capacity is C=dU/dT The...

Hi, I want to calculate heat capacity of anharmonic oscillator in one dimension. Does anyone have an idea? Thanks...

Can someone tell me if there is a difference in the moving motion between a quantum harmonic oscillator and a simple harmoic oscillator. Also, does anoyone know a good site where i could learn more on quantum harmonic oscillator. ty

The frequency of a harmonic oscillator is (as you know) f=\frac{1}{2\pi}\sqrt{\frac{k}{m}} I am wondering if this equation only applies for massless harmonic oscillators (or oscillators oscillating sideways)? The proof for the equation above is \sum {F=ma} -kx=ma...

The question is as follows: Suppose that, in a particular oscillator, the angular frequency w is so large that its kinetic energy is comparable to mc2. Obtain the relativistic expression for the energy, En of the state of quantum number n. I don't know how to begin solving this question. I...

proove that the average energy of a quantum oscillator = hw/(e^(hw/kT)-1) where h= h bar w=omega k=boltzmann constant T=temp

Homework Statement "Two non-interacting particles are placed in a one-dimensional harmonic oscillator potential. What are the degeneracies of the two lowest energy states of the system if the particles are a)identical spinless bosons b)identical spin-1/2 fermions? Homework Equations...

Homework Statement I am having a bit of trouble with a homework problem on relaxation oscillators, the schematic is shown below: https://webspace.utexas.edu/sz233/Relaxation%20Oscillator.png The original problem states: derive a relationship for the period of oscillation for a relaxation...

Hi, Why is it that the WKB approximation produces the correct eigenvalues for the Harmonic Oscillator problem, but the wrong wavefunctions, whereas for the square well, we get correct wavefunctions and the wrong eigenvalues? I've been trying to dig through the approximations we make in...

Homework Statement Show: \psi_1=N x e^{-\frac{x^2}{\sigma}} is an eigenfunction of the total energy operator(H). Homework Equations psi=N x exp[-x^2/K]The Attempt at a Solution I plugged in the above to the Schrodinger Equation-time indep. for Harmonic oscillator but I keep getting an x^2...

moved to Advanced Physics Section seemed more relevant link to it is https://www.physicsforums.com/showthread.php?p=2169513#post2169513" Sorry for the double post in two spots if this can be removed Thanks Heeps

The one dimensional harmonic oscillator is associated with the group U(1) and the three dimensional harmonic oscillator is associated with the group SU(3). Is their a group associated with the two dimensional harmonic oscillator? Thank you for any thoughts.

I've recently purchased a book on Quantum Physics, and I'm trying to get the basics down. At this point in time, I'm reading up on how Planck proposed that oscillators can only oscillate at discrete energies as opposed to on any amount of energy (on a theoretical continuous spectrum). This came...

The 3-dimensional harmonic oscillator has SU(3) symmetry. This is stated in many papers. It seems to be due to the spherical symmetry of the system. (After all, the idea of a 3d harmonic oscillator is that a mass is attached to the origin with a spring, and that the mass can move in 3...

A 2.6 kg block is attached to a horizontal spring and undergoes simple harmonic motion on a frictionless surface according to the graph shown above. (a) What is maximum velocity of the box? (b) What is the mechanical energy of the box? now the wave is -sin wave but crosses the x-axis...

Homework Statement Hi guys the question is: a mass spring-damper system is positioned between two rigid surfaces, if mass m = 200g, spring constant k = 80 Nm-1, and damping pot of coefficient 65 gs-1. The mass is pulled 5cm down from its equilibrium position and then released. What is the...

Homework Statement The wave function \Psi(x,t) ofr the lowest energy state of simple harmonic oscillator, consisting of a particle mass m acted on by a linear restoring force F=Cx, where C is the force constant, can be expressed as.. \Psi(x,t)=Aexp[-(\sqrt{}Cm/2h)x^{}2-(i/2)(\sqrt{}C/m)t]...

Homework Statement Suppose there is a square plate, of side a and mass M, whose corners are supported by massless springs, with spring constants K, K, K, and k <= K (the faulty one). The springs are confined so that they stretch and compress vertically, with unperturbed length L. The...

Homework Statement Hi all. At time t<0 a particle is in the stationary state \left| {\psi _0 } \right\rangle of the harmonic oscillator with frequency omega1 (i.e. the ground state of the H.O.). At t=0 the Hamiltonian changes in such a way that the new angular frequency is omega =...

Design a digital ring oscillator using logic inverters that have propagation delay times of tPLH = 28ns and tPHL = 42ns. The Attempt at a Solution I'm using a general ring oscillator design using 3 CMOS inverters like this...

Homework Statement A damped harmonic oscillator is driven by a force F external= F sin (omega * t) where F is a constant, and t is time. Show that the steady state solution is given by x(t)= A sin (omega * t - phi) where A is really A of (omega), the expression for the amplitude...

How to find the probability density function of a simple harmonic oscillator? I know that for one normal node is should be a parabola but what is the formula and how do we derive it?

Homework Statement a 200g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t=0s, the mass is at x=5.0 cm and has v=-30 cm/s. Determine: a) period b)angular frequency c) AMPLITUDE Homework Equations x(t)=Acos(wt+psi) v(t)=-Awsin(wt+psi) w=2*pi*f T=1/f...

Thanks for all the help on the first question but now I have to solve for <T>. I have no idea how to do this, and I could use some help for a kick start. thanks!

first post! but for bad reasons lol Im trying to find <x> and <p> for the nth stationary state of the harmonic potential: V(x)=(1/2)mw^2x^2 i solved for x: x=sqrt(h/2mw)((a+)+(a-)) so <x> integral of si x ((a+)+(a-)) x si. therefor the integral of si(n+1) x si + si(n-1) x si. si(n+1)...

Why the LC oscillator ckt. is also known as a TANK ckt.?

In quantum mechanics, one of the major concerns is the propagator determination of the system. The propagator is completely expressed in terms of its classical in the Van-Vleck Pauli Formula. In a harmonic oscillator in a time dependent force, the Lagrangian is given by...

Hi all! I was considering the Energy of a driven damped oscillator and came upon the following equation: given the equation of motion: m\ddot x+Dx=-b\dot x+F(t) take the equation multiplied by \dot x m\ddot x\dot x+Dx\dot x=-b\dot x^2+F(t)\dot x and we rewrite it...

One application of an opamp can clearly be seen from a set of speakers for instance, but what about an oscillator circuit? What would be a good, clear, example of an application of an oscillator?

Homework Statement What
 is 
the 
wavelength 
of 
the 
emitted
 photon 
when
 HCl
 de‐excites 
from
 the
 first vibrational 
state? Well, I had to solve for the energy of the first vibrational state in the question before, assuming that it behaved like a harmonic oscillator using the...

damped harmonic oscillator, urgent help needed! Homework Statement for distinct roots (k1, k2) of the equation k^2 + 2Bk + w^2 show that x(t) = Ae^(k1t) + Be^(k2t) is a solution of the following differential equation: (d^2)x/dt^2 + 2B(dx/dt) + (w^2)x = 0 Homework Equations The...

If a mass that hangs suspended vertically from a spring is increased, then won't the period increase as a direct linear proportion? (Because the larger mass has a greater inertia and will require a larger force and longer time to change the direction of motion on each oscillation?) Some...

1. Homework Statement and the attempt at a solution Please see attached. I'm not so sure if my problem lies with the physics or the mathematics. I have the distinct feeling that it's the latter and that I'm missing something elementary, but truly have no idea how to proceed. Any...

Hello, how do I compute the transition amplitude of the forced harmonic oscillator with the method of path integration? Regards, Mr. Fogg

Homework Statement Show that, [a, \hat H] = \hbar\omega, [a^+, \hat H] = -\hbar\omega Homework EquationsFor the SHO Hamiltonian \hat H = \hbar\omega(a^+a - \frac{\ 1 }{2}) with [a^+, a] = 1 [a, b] = -[b, a] The Attempt at a Solution I have tried the following: [a, \hat H] = a\hat...

Homework Statement This is supposed to be a question for high school seniors who've had instruction in introductory concepts of special relativity and non-relativistic QM. According to my TA, he isn't too certain if it can be done within these confines but nonetheless I've attempted the...

I have the following equation subject to y(0)=0 and y'(0) = 0 my'' + b y' + k y = C I have done an experiment where I measured force at given depth for a dampened harmonic oscillator. Is it possible to use the force I measured to solve for displacement and then back out coefficient b for...

Homework Statement If you have a simple harmonic oscillator based on a spring of force constant 5.79 N/m, with an attached mass of 0.828 kg, and the oscillator is initially displaced 3.5 cm from equilibrium, at what distance from the equilibrium point (in cm) will the oscillator have equal...

Homework Statement Not actually a homework problem, just something from my book I'm trying to verify. Homework Equations The general form of the equation for damped oscillations... \ x(t) = e^{-\gamma t}(Ae^{\sqrt{\gamma^{2}-\omega^{2}}t}+Be^{-\sqrt{\gamma^{2}-\omega^{2}}t}) Here gamma =...

A 50.0-g mass connected to a spring with a force constant of 35.0 N/m oscillates on a horizontal, frictionless surface with an amplitude of 4.00 cm. Find the speed of the mass when the displacement is 1.00 cm. Can I use here something like : \frac{mv2}{2}=0,5kx2?

Many quantum physics/chemistry books use Schrodinger's equation to derive a differential equation which describes the possible wavefunctions of the system. One form of it is this: \frac{d^{2}\psi}{dx^{2}} + (\lambda - a^{2}x^{2})\psi = 0 "a" and lambda are constants. Most books solve this...

How to describe a harmonic oscillator defined by H(q,p) = \frac{p^2}{2m} + \frac{1}{2}kq^2 in a heat bath with some fixed temperature T? I suppose this question alone is not quite well defined, because it mixes classical and statistical mechanics in confusing manner, but I thought that one...

Homework Statement A 300g oscillator has a speed of 95.4 cm/s when its displacement is 3.0 cm and 71.4 cm/s when it displacement is 6.0 cm. What is the oscillator's maximum speed? Homework Equations x = Acos(\omegat + \phi) v = -\omegaAsin(\omegat + \phi) vmax = \omegaA v =...

Homework Statement A 284 g oscillator has a speed of 94.86 cm/s when its displacement is 2.98 cm and 74.06 cm/s when its displacement is 5.92 cm. What is the oscillator's maximum speed? Homework Equations Vmax=2pi*f*A The Attempt at a Solution confused as to wat the AMP would be