Harmonic oscillator Definition and 743 Threads

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Homework Statement Calculate the probability for finding the ground state harmonic oscillator beyond its classical turning points. Homework Equations Psi n(q) = (alpha/pi)^(1/4) exp(−alpha*q^(2)/2), where alpha = (kμ)^(1/2)/h bar The Attempt at a Solution i know it's going to be...

1. The equation of motion is Ma(t) +rv(t) + Kx(t)=0 a) Look for a solution of this equation with x(t) proportional exp(-Ct) and find two possible values of C. Homework Equations 3. No clue... Please help if you can!

Hello friends: I do not understand why when solving the undamped harmonic oscillator equation dx/dt+w02x=Fcoswt I am allowed to neglect the homogeneous solution. I read that in a damped harmonic oscillator if you let the time pass, the homogeneous solution will disappear and you will...

Homework Statement Is there any way to find <\varphi_{n}(x)|x|\varphi_{m}(x)|> (where phi_n(x) , phi_m(x) are eigenfunction of harmonic oscillator) without doing integral ? Homework Equations perhaps orthonormality of hermite polynomials ...

Hi. I have recently designed a simulator about Qunatum Mechanics one dimensional harmonic oscillator. Please try it. I will be glad to read your opinions. http://erham.persiangig.ir/Programs/1386/QM1DHOS10.png Size: 223 KB http://erham.persiangig.ir/Programs/1386/QM1DHOS10.zip"

Homework Statement In a diatomic molecule with atom masses m1 and m2, the atoms are bound by a potential V(r)=V_0\big[ \big(\frac{r_0}r\big)^{12} - 2\big(\frac{r_0}r\big)^{6}\big] where r is the distance between the atom centra, r0 is the equilibrium istance, and V0 is a constant depending...

Homework Statement For a 1D QM harmonic oscillator, (a) the discrete energy states are nhw (b) the discrete energy states are (n+0.5)hw (c) the lowest energy state wave function is ~\exp^\frac{-\alpha^2\ x^2}{2} (d) the probabilty of finding the particle outside the classical...

[SOLVED] Perturbation of the simple harmonic oscillator Homework Statement An additional term V0e-ax2 is added to the potential of the simple harmonic oscillator (V and a are constants, V is small, a>0). Calculate the first-order correction of the ground state. How does the correction change...

Hi folks, I wonder if I could run a few things past the quantum gurus among you - I'm just not quite convinced of some of the results I've been deriving. Homework Statement Consider the ground state of the simple harmonic oscillator at t = 0 with the normalised wave function...

Homework Statement particle in ground state of 1D harmonic oscillator - spring constant is doubled - what is the probability of finding the particle in the ground state of the new potential Homework Equations v=1/2kx^2 oscillator potential wavefunction ground state n=0 =...

Two particles are subjected to the same potential V=\frac{m \omega x^2}{2}. Particle one has with position x1 and momentum p1. Particle two has with position x2 and momentum p2. The problem asks how to show that the Hamiltonian is H=H_1+H_2 I am assuming that it is asking for a way to derive...

[SOLVED] QM simple harmonic oscillator Homework Statement If I have a particle in an SHO potential and an electric field, I can represent its potential as: V(x) = 0.5 * m \omega^2 (x - \frac{qE}{mw^2})^2 - \frac{1}{2m}(\frac{qE}{\omega})^2 I know the solutions to the TISE...

I was just wondering what the difference was in the 1-D simple harmonic oscillator in the Heisenberg picture versus the Schrodinger picture?

In the case of an undamped oscillator, the work done by the system is written as ( assume initial position is 0 ) : W = - \Delta U = - K \frac{x^2}{2} But to verify this , we must assume that the force acting on the oscillator is constant , which is not true as F = f(x) according to...

Homework Statement Use ladder operator methods to determine the kinetic and potential energy of eigenstates of the harmonic oscillator.Homework Equations H=\frac{p^2}{2m} + \frac{1}{2}m\omega x^2 x=\sqrt{\frac{\hbar}{2m \omega}}(a+a^{\dagger})The Attempt at a Solution So I squared x, and then...

Homework Statement The turning points of a classical harmonic oscillator occur when the potential energy is equal to the total energy, correct? Homework Equations The Attempt at a Solution

Find the find the eigenfunctions and eigenvalues of a two-dimensional isotropic harmonic oscillator. I don't understand what does isotropic here mean. isotropic can be defined "not changing" when the coordinate change to any other position. Am I correct? Like mass, pressure...

Uncertainty - Harmonic Oscillator The Wave function for the ground state of a quantum harmonic oscillator is \psi=(\alpha/\pi)^{1/4}e^{-\alpha x^2/2} where \alpha = \sqrt{ mk/ \hbar^2} . Compute \Delta x \Delta p known: Heisenberg Uncertainty Principle: \Delta p \Delta x >= \hbar/2...

i m in a real problem and hav to give answers to the following problem tomorrow..please anyone help me.. Q: show that in ground state of linear harmonic oscillator ,the probability of finding oscillator outside the classical limit is nearly 17%?

looking at the quantum mechanical harmonic oscillator, one has the differential equation in the form: \frac{d^2\psi}{du^2}+(\alpha-u^2)\psi=0 when a person who doesn't know any physics sees the equation, he will try a serial solution for psi, and he will find a solution with some recursive...

Can someone explain to me how they went from U(x)=(1/2)kx^2 to E=(n+1/2)(h/2pi)w? http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc.html

Defining the state | \alpha > such that: | \alpha > = Ce^{\alpha {\hat{a}}^{\dagger}} | 0 >\ ,\ C \in \mathbf{R};\ \alpha \in \mathbf{C}; Now, | \alpha > is an eigenstate of the lowering operator \hat{a}, isn't it? In other words, the statement that \hat{a} | \alpha >\ =\ \alpha | \alpha >...

Hi, I am approximating a proton transfer from one water molecule to another. I would to have a quantum mechanical description of the proton transfer as a wavefunction. So I have approximated a "transition state" and use this as a harmonic potential. Then I get some energy values around this...

Homework Statement Find the energy levels and the wave functions of two harmonic oscillators of mass m_1and m_2, having identical frequencies \omega, and coupled by the interaction \frac{1}{2}k(x_{1}^{2}-x_{2}^{2})^2 Homework Equations Schrodinger equation. The Attempt at a...

Homework Statement Use Frobenius’ method to solve the problem of the isotropic three dimensional harmonic oscillator in polar coordinates. It is sufficient to find the energy levels and degeneracies, but it would be nice to plot the spectrum like we did for hydrogen. Be sure to introduce...

Hi! I'm trying to calculate the degeneracy of each state for 3D harmonic oscillator. The eigenvalues are En = (N + 3/2) hw Unfortunately I didn't find this topic in my textbook. Can somebody help me?

The problem is the following: a.) Obtain the equation of motion for the very small oscillations of a bead of mass m attached 1/5th of the way along a massless string of length 5l, which is under tension T. b.) Hence show that the angular frequency of oscillation is omega=sqrt(5T/4ml)...

Homework Statement Show that the fractional energy lost per period is \frac{\Delta E}{E} = \frac{2\pi b}{m\omega_0} = \frac{2\pi}{Q} where \omega_0 = \srqt{k/m} and Q = m\omega_0 / b Homework Equations E = 1/2 k A^2 e^{-(b/m)t} = E_0 e^{-(b/m)t} The Attempt at a Solution \Delta E = 1/2 k A^2...

Homework Statement Show taht neither \Delta x nor \Delta p is generally constant (independant of time) for a general state of the one dimensional harmonic oscillator. Prove that (\Delta x)^2 and (\Delta p)^2 are both of the form (\Delta)^2 = A + B \cos^2 \omega t where omega is the...

Hello, A harmonic oscillator is in the initial state: Psi(x, 0) = Phi_n (x) where Phi_n(x) is the nth solution of the time-independent Schr¨odinger equation. What is Psi(x, t)? Any clue? Thanks

Hi, Is there an explicit formula for the eigenfunctions of the harmonic oscillator? By explicit, I mean "not written as the nth power of the operator (ax-d/dx) acting on the ground state". Thanks.

Homework Statement The covalent bond between the two protons in the H2 molecule can be modeled by a harmonic spring with a spring constant k = 1100 N/m. a. What is the zero point energy of the H2 molecule as a harmonic oscillator? b. What is the energy of the first excited state...

A mass m moves along the x-axis subject to an attractive force given by \frac {17} {2} \beta^2 m x and a retarding force given by 3 \beta m \dot{x}, where x is its distance from the origin and \beta is a constant. A driving force given by m A \cos{\omega t} where A is a constant, is applied to...

Driven Damped Harmonic Oscillator, f != ma?? Let's say I've got a driven damped harmonic oscillator described by the following equation: A \ddot{x} + B \dot{x} + C x = D f(t) given that f = ma why can't I write A \ddot{x} + B \dot{x} + C x = D ma substitute \ddot{x} = a to get A \ddot{x}...

the problem is as follows: in the ground state of the harmonic oscillator what is the probabilty of finding the particle outside the classically allowed region. where the classically allowed nrg is given by E=(1/2)m*omega^2*a^2 (where a is the amplitude). were given that...

I'm trying to find the work done by a harmonic oscillator when it moves from x_{0} = 0 m to x_{max} = 1 m. The oscillator has initial velocity v_{0}, a maximum height of x_{max} = 1 m, initial height of x_{0} = 0 m, a spring constant of k, a mass of m = 1 kg, and a damping factor of b. It can...

Homework Statement We have a first frame S (named coordinate frame) at rest on the Earth (we suppose a non-rotating earht and this frame as a perfect inertial frame) and a second frame S' (named proper frame) moving in respect to the first with a constant relativistic velocity V along the...

Homework Statement A linear harmonic oscillator is subject to friction(stokes). The Oscillator gets an Impulse at the time t = 0 at the rest position. What is the equation of motion for the time interval 0 - t0?Homework Equations Friction force: Fr = -a * x'(t); a = constant (stokes friction)...

bah nevermind the question is too complicated to even write down :cry: i hate this :(

A simple harmonic oscillator consists of a block of mass 2.60 kg attached to a spring of spring constant 380 N/m. When t = 2.30 s, the position and velocity of the block are x = 0.148 m and v = 4.080 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity...

I'm given that there is a harmonic oscillator in a state that is a superposition of the ground and first excited stationary states given by \psi = \frac{1}{\sqrt{2}}\abs{\psi_0(x,t) + \psi_1(x,t)}, where \psi_0 = \psi_0(x)e^{\frac{-iE_0t}{\hbar}} and \psi_1 = \psi_1(x)e^{\frac{-iE_1t}{\hbar}}...

I've been told (in class, online) that the ground state of the 3D quantum harmonic oscillator, ie: \hat H = -\frac{\hbar^2}{2m} \nabla^2 + \frac{1}{2} m \omega^2 r^2 is the state you get by separating variables and picking the ground state in each coordinate, ie: \psi(x,y,z) = A...

I worked these problems out: [x, H] = xH - Hx = 0 [p, H] = pH - Hp = non-zero H is the harmonic oscillator Hamilitonian, x and p are the position and momentum operators, respectively. My question is, why doesn't p commute with H, but x does?

Ok - here goes: I see the energy levels of the harmonic oscillator as E = hw(n+1/2) = hwn + hw/2 (please ignore the lack of cool symbols) Now the hw/2 is something called the ground state - fine - no problem. Should I interpret homework as the fundamental harmonic? 2hw as the...

Hello... We have 3 fermions (s=1/2) at the ground state of a harmonic oscillator moving over the x-axis with a the classic hamiltonian for a three particle oscillator : H =(1/2m)*(P1)^2 +((1/2)*m(w^2)((x1)^2)) +(1/2m)*(P2)^2 +((1/2)*m(w^2)((x2)^2)) +(1/2m)*(P3)^2 +((1/2)*m(w^2)((x3)^2)) we...

Suppose I have 4 bosons in a one-dimensional harmonic oscillator potential and that the total energy is E_\text{tot} = 8 \hbar \omega. Recall, E_n = (n+1/2)\hbar\omega. Question: How many quantum states exist? (assume no spin degeneracy) After accounting for the ground state, we have 6...

energy values of a "half" harmonic oscillator This is the full question: Find the solution to the "half" harmonic oscillator: http://img241.imageshack.us/img241/9181/02bt7.jpg Compare the energy values and wave functions with those of the full harmonic oscillator. Why are some of the full...

Hello all, if I have an ion trapped in a harmonic oscillator potential with a resonant frequency 0f 11 MHz and the ion cooled to a temperature of T=0.48mK, how do I find the probability that the oscillator is in its ground state? I know that the ground state energy is 1/2 \hbar \omega, but...

Hey! Can someone explain to why the energy of the harmonic oscillator must be at least: \frac{(\Delta p)^2}{2m}+\frac{1}{2}m \omega^2 (\Delta x)^2 I mean, \Delta x and \Delta p represents the uncertainty in the position and momentum, and therefore it does not really have anything to do...