Oscillator Definition and 1000 Threads

Homework Statement Using the equations that are defined in the 'relevant equations' box, show that $$\langle n' | X | n \rangle = \left ( \frac{\hbar}{2m \omega} \right )^{1/2} [ \delta_{n', n+1} (n+1)^{1/2} + \delta_{n',n-1}n^{1/2}]$$ Homework Equations $$\psi_n(x) = \left ( \frac{m...

Hi, What is the physical meaning of zero probability of finding a particle in the square of the Quantum SHO wave function? the particle is supposed to oscillate about the equilibrium position, how would it go from an end point to the other end point without passing by certain points? Could the...

Hey, I'm stuck halfway through the solution it seems. I could use some tips on how to continue. 1. Homework Statement I have to determine a linear combination of the states |0\rangle, |1\rangle, of a one dimensional harmonic oscillator, so that the expectation value \langle x \rangle is a...

Homework Statement What is the normalized ground state energy for the 3-D Harmonic Oscillator Homework Equations V(r) = 1/2m(w^2)(r^2) The Attempt at a Solution I started with the wave fn in spherical coordinates, and have tried using sep of variables, but keep getting stuck when trying to...

I was wondering whether it's possible to write a code in C++ that would be able to solve the Harmonic Oscillator: \ddot{x} + \gamma x = F_{external}(t,x) With different F function inputs... I thought about creating a function with if clauses, so for different inputs by the user, the force F...

Given the half harmonic potential: \begin{equation}V=\begin{cases}1/2\omega^2mx^2 & x > 0\\\infty & x < 0\end{cases}\end{equation}What will be the Hamiltonian of the half oscillator?I understand that for x>0 the Hamiltonian will be...

I was wondering why the average kinetic energy is calculated in this manner. They are dividing the kinetic energy function by the period (noted here as To) and integrating it with limits from 0→To. Why? (This is a tiny portion of a larger textbook example, not an actual assignment.) Sorry for...

Voltage = 9.0 V, Current = 20 mA, Capacitor (C) = 10 microF, Resistance before (too high) [R_A = R_B] = 10 k Ohms. In a a-stable oscillator, calculating the resistance needed for two resistors (R_A = R_B) to discharge and charge a capacitor (C) so that a LED does not blow. Currently my circuit...

Homework Statement The transition amplitude for the harmonic oscillator may be written as ##\langle x_2, t_2 | x_1, t_1 \rangle = N_{\omega}(T) \exp(i/\hbar S_{cl})##, where ##T=t_2-t_1## and ##S_{cl}## is the classical action. Let the wave function at ##t=0## be ##\psi(x,o) =...

Homework Statement A particle of mass m in the one-dimensional harmonic oscillator is in a state for which a measurement of the energy yields the values ##\hbar\omega/2## or ##3\hbar\omega/2## each with a probability of one-hald. The average value of the momentum ##\langle p_x\rangle## at...

So I built a 555 astable oscillator. I wanted to get 50 KHz on my output, which I have achieved, but the values of my components do not match the formula I have calculated. I have: R1 = 98 ohms R2 = 67 ohms Cap = 100nF So I have: 1.44/(98 + 2 67) 100nF Which should be 62KHz. Also can anyone...

I have the following circuit that I need to calculate the voltage across the capacitor as a function of time. Standard variables for the component values, voltage drops, currents, ect. You'll notice that the voltage (at the top right corner) oscillates at a frequency dependent on the...

For the harmonic oscillator in 1-D we get the 2nd time derivative of the x Heisenberg operator = -ω2 x. When that is integrated it gives xH (t) = Acos(ω t) +Bsin (ω t) where A and B are time independent operators. My question is why are the constants A and B incorporated into the terms as a...

I'm trying to figure out how to derive the equations for Energy from the differential equation corresponding to the (simple and damped) harmonic oscillator. Please note that I don't want to start with the expressions for kinetic and potential energy, I want to derive them. The references that I...

Hello, I'm was going through the simple harmonic oscillator, just as a recap, and I stumbled upon something which is causing me wonder. I'm solving the SHO with a shifted origin, and so I have the differential equation F=-k(x-x_0) \ddot{x}=-\frac{k}{m}x+\frac{kx_0}{m} Now, I get that I can...

Homework Statement Hello, I'm just curious as to whether I'm going about solving the following problem correctly... Problem Statement: A particle mass m and charge q is in the ground state of a one -dimensional harmonic oscillator, the oscillator frequency is ω_o. An electric field ε_o is...

Homework Statement Find eigenvalues and eigenvectors of a perturbed harmonic oscillator (H=H0+lambda*q4 numerically using different numerical methods and plot perturbed eigenfunctions. I wrote a code in c++ which returns a row of eigenvalues of the perturbed matrix H and a matrix of...

I've always just accepted that as you scale down a mechanical system the frequency and Q factor both increase. For example, this Wikipedia page simply says that "Small bells ring at higher frequencies than large bells". But for a driven damped harmonic oscillator, what is the exact relationship...

Homework Statement Find the initial conditions for 2 interchangeable harmonic oscillators (undamped) so that they have the same amplitude of oscillation. Homework Equations x(t)=Xm*cos(wt+ϕ)The Attempt at a Solution The amplitude of the function is given by Xm so I would have thought that just...

Homework Statement Given a harmonic oscillator with mass m, and spring constant k, is subject to damping force F= cdx/dt and driven by an external force of the form F[ext]= FoSin(wt). A) Find the steady state solution. B) Find the amplitude and the phase. Homework Equations F=-kx the steady...

I seem to have two approaches that I've seen and understand, but I can't quite see how they relate. 1. Write a general time evolving state as a superposition of stationary states multiplied by their exp(-iEt/h) factors, and calculate <x>. We find that <x>=Acos(wt+b) as in classical physics (in...

Homework Statement I'm required to design a simple ring oscillator... One with three stages of cascaded cmos inverters using pspice capture(student version) Homework EquationsThe Attempt at a Solution I have simulated the circuit with a 5v supply but all i see is a dc line at 2.50v.has this...

Hello everyone! Seeing as this is my first post, I'll give you a basic background of who I am: My name is Andrew Raisbeck; I graduated from university with a Bachelor of Computing (Computer Science) degree a little over a year ago, and I now work full-time for the government of Canada. Since I...

Hello, I was just watching a youtube video deriving the equation for the Hamiltonian for the harmonic oscillator, and I am also following Griffiths explanation. I just got stuck at a part here, and was wondering if I could get some help understanding the next step (both the video and book...

Hello, I juste don't know how this was done it is on the solutionnary of a very long exercise and i am not getting this calculation 1. Homework Statement <1,0| ax+ay++ax+ay+axay++axay|0,1> = <1,0|1,0> Homework Equations 3. The Attempt at a Solution We have that |0,1> = ay+ |0,0> I don't...

All, I am confused as to exactly how the capacitive relaxation oscillator works. From the diagram above: Because the lamp is in parallel, why is it not immediately receiving the voltage necessary to light instantly? Thanks.

Homework Statement [/B] The isotropic harmonic oscillator in 2 dimensions is described by the Hamiltonian $$\hat H_0 = \sum_i \left\{\frac{\hat{p_i}^2}{ 2m} + \frac{1}{2} m\omega^2 \hat{q_i}^2 \right\} ,$$ for ##i = 1, 2 ## and has energy eigenvalues ##E_n = (n + 1)\hbar \omega \equiv (n_1 +...

Hi Guys, I'm looking into the Lorentz model Since the acceleration/de-acceleration of electron can cause radiation hence create force, can anyone tell me how to modify the above equation to include the term of radiation force? Thanks. jack

Hi All! A little background info. I'm working with cardiac pacemaking devices with the overall scope of implementing piezoelectric energy harvesters into the devices. I'm in the initial stages of research and development. Okay, so this is my conundrum: I have an output pulse circuit as shown...

Homework Statement I must find the average number of energy levels of quantum harmonic oscillator at temperature T, and the answer is given as I must use Boltzmann distribution and the sum of geometric progression. For finding the average value I must use the equation <F>=trace(F*rho)...

Homework Statement A mass m sits on a horizontal frictionless surface and is attached to a wall by means of a spring having force constant k. The mass is now subjected to an additional force of the form. F(t) = Acosbt (a) Write the equation of motion for this mass.(b) What is the solution to...

As I was playing around with a small AM oscillator, I thought it would be time to understand how they actually work. I am referring to the 3rd picture on this page (base mode): http://elektroniktutor.oszkim.de/signalkunde/colpitts.html Given the working point of the transistor, I describe its...

Homework Statement Given characteristic equation for a circuit containing a diode, I must figure out how to fit a polynomial to the curve so that the van der pol equation is obtained. The paper I am reading is here: http://www.unige.ch/math/hairer60/pres/pres_rentrop.pdf My doubts are...

1. After finding out that the wave function ##\Psi(z) \sim Ae^{\frac{-z^{2}}{2}}## in the limit of plus or minus infinity Griffiths separates the function into two parts ##\Psi(z)=h(z)e^{\frac{-z^{2}}{2}}## My question will be about a certain aspect of the function ##h(z)## After solving the...

Hi everyone. On these days, by watching solar panels and similar stuff, I just thought about it, and why they take such a wide surface to produce energy, and why their output is often low, as we all know. By navigating here on the internet, I've just seen a device called OPO (Optical...

[FONT=Georgia] Hi, I'm trying to simulate exercise 13.21(a) from Sedra-Smith, with: Vcc=5V f=100 kHz [FONT=Georgia]and the following BJT model: .model modn NPN(Is=6.734f Xti=3 Eg=1.11 Vaf=74.03 Bf=416.4 Ne=1.259 Ise=6.734f Ikf=66.78m Xtb=1.5 Br=.7371 Nc=2 Isc=0 Ikr=0 Rc=1 Cjc=3.638p Mjc=.3085...

My problem is described in the animation that I posted on Youtube: For the sake of convenience I am copying here the text that follows the animation: I have made this animation in order to present my little puzzle with the quantum harmonic oscillator. Think about a classical oscillator, a...

Homework Statement Damping is negligible for a 0.164 kg mass hanging from a light 6.70 N/m spring. The system is driven by a force oscillating with an amplitude of 1.77 N. At what frequency will the force make the mass vibrate with an amplitude of 0.500 m? There are two possible solutions...

Homework Statement An oscillator with mass 0.5 kg, stiffness 100 N/m, and mechanical resistance 1.4 kg/s is driven by a sinusoidal force of amplitude 2 N. Plot the speed amplitude and the phase angle between the displacement and speed as a function of the driving frequency and find the...

Homework Statement Calculate how much original energy the oscillator in will have left after three cycles. Using Q= (ω/Δω) I have calculated the Q factor to be 4 Homework Equations The answer can be obtained by using the equation Q=2π(E/ΔE) Where ΔE/E is the fractional energy loss per...

Homework Statement I'm trying to hook up crystal oscillator package on breadboard and test for expected operation: I'm not sure how and cannot find any data sheets for the pin connection diagrams, I attached an image I found of the kind of package I'm using. There are four pins. Homework...

Homework Statement Given the coherent state of the harmonic oscillator |z>=e^{-\frac{|z|^2}{2}}\sum_{n=0}^\infty\frac{z^{n}}{\sqrt{n!}}|n> compute the probability for finding n quanta in the sate |z> and the average excitation number <z|n|z>Homework Equations...

Homework Statement estimate the value of turn-ratio n [/B] R1=4.7 kΩ, R2=24 kΩ, Rl=2.7 kΩ, hfe=250, hoe=10^-5, hie=4 kΩ Homework Equations loop gain=1/n[hfe/hie*R'l] R'l=Rl||hoe||[n^2(R1||R2)] [/B] The Attempt at a Solution loop gain=1 [/B]

for harmonic oscillator, V(x) = 1/2*m*w^2*x^2. here, the spring can be stretch or compress. however, is if the spring can only stretch such that V(x) is infinity for x<0, then find energy level for this setup. I don't understand the part about spring only being able to stretch. what does that...

Homework Statement There is a harmonic oscillator with charge q and sudenly we turn on external electric field E, which direction is the same as oscillator's. We need to find probability, that particles energy calculated in electric field will be in m state. n=1, m=2 2. Homework Equations The...

Homework Statement what is the energy loss of the damped oscillator. Homework Equations x(t) = A*e^(-Bt)*cos(w1*t) T = 1/2 mv^2 The Attempt at a Solution To solve for an undamped oscillator, I took the derivative of the equation of motion x(t) and plugged the amplitude into 1/2 mv^2 equation...

Homework Statement The problem requires to solve the integration to find ## G(t) ## after ##G(\omega)## is found via Fourier transform. We have G(\omega)= \frac{1}{2\pi}\frac{1}{\omega _{0}^2 - \omega ^2} Homework Equations As mentioned previously, the question asks to find ##G(t)## The...

in my previous thread i was trying to build a sine oscillator and an amplifier. decided to give up on the idea and purchase. any chips out there that can give me 30-40volts peak to peak. the frequency is not an issue as long as it is above 1 MHz. i guess i can use any crystal oscillator as long...

I'm trying to determine the frequency of this oscillator . The traditional resonant frequency equation for the tank circuit doesn't give the correct answer as the feed back capacitor effects the circuit . i would also like to know what the feedback capacitor does? any help would be great.

Homework Statement A particle of mass m in the harmonic oscillator potential V(x) = (mω2x2)/2 is described at time t = 0 by the wavefunction χ(x, t = 0) = 1/[(2πσ2)1/4] exp[-x2/(4σ2)] What is <E> at time t? Homework EquationsThe Attempt at a Solution <T>+<V>= <E> I've found the expectation...