Question: 1. Consider a simple one-dimensional harmonic oscillator and assuming that at time t = 0 the state of the system is given by the

1. Consider a simple one-dimensional harmonic oscillator and assuming that at time

1. Consider a simple one-dimensional harmonic oscillator and assuming that at time t = 0 the state of the system is given by the wave function 4 Tab(0)) = V50 p0(x) + (2) + 50 02(x) V50 where is understood by on (x) the autofunction corresponding to the n - th excited state of the oscillator harmonic. for (a) Find the wave function |(t)) for t> 0. (b) Find the mean value of the energy for t> 0. (c) Obtain the mean value of the impulse as a function of time (p(t). (d) Calculate the probability of finding the system in the initial state in an instant t > 0.

Step by Step Solution

★★★★★

3.42 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Follow ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Physics Questions!

The impulse response of an LTI system is given by h(n) = (n) (n k0). To determine the impulse response g(n) of the inverse system, an engineer computes the determine N-point DFT H (k), N = 4k0, of...

Consider the following biochemical reactor. The kinetics of the system is given by the following Monod model. HmaxS K, +S The rate of biomass produced is ri (units- mass of cells generated per unit...

The voltage across a 2-?F capacitor is given by the wave form in figure. Compute the current waveform. v(t) (V) 2 3 t (ms) -12

Linda Stanley is the Vice President for Computing and Information Services at State University (SU), a large, urban university that has experienced a 3% growth in enrollments every year for more than...

Figure shows a two-phase hybrid stepping motor with castleated poles on the stator. The rotor is shown in the position it occupies when current is flowing into the positive lead of phase 1. a. If...

Consider a one dimensional harmonic oscillator of Hamiltonian where x and p are Lagrange conjugate variables. 1.We set x = X/ m and p = P m. Write the expression of the Hamiltonian in terms of X and...

Consider the one dimensional harmonic oscillator with angular frequency $\omega$ perturbed by the small non-linear potential $\epsilon q^{4}$. (a) Find the solution using the perturbation...

This is a theoretical physcis question, please answer clearly The wavefunction of a particle of mass m in the first excited state of a one- dimensional harmonic oscillator with classical frequency w...

Consider the acid-catalyzed reaction Deduce the rate law and show that it can be made independent of the specific term [H+]. (1) HA +H* HAH (2) HAH* +B- BH* + AH k,k, both fast k, slow

A Capacitor Burglar Alarm The capacitance of a capacitor can be affected by dielectric material that, although not inside the capacitor, is near enough to the capacitor to be polarized by the...

Notes to financial statements provide: Discussions that further explain items shown in the financial statements. Comparative financial information with the previous year. Management's discussions...

A 41.41-mL sample of a 0.1250 M acid reacts with an excess of Na2CO3 to form 150.0 mL CO2 at 646 mmHg and 27oC. If the acid is either HCl or H2SO4, which is it?

Which of the following authorizes the broker to act as agent in securing a purchaser for the seller's property and calls for a payment to the broker only if he / she were instrumental in finding the...

Harrison Company has a July 31 fiscal year end and uses a perpetual inventory system. The records of Harrison Company show the following data: After its July 31, 2017, year end, Harrison discovered...

(a) What suggestions can you offer Nina when she gets home from work and wants to discuss with herhusband her likely career promotion? (b) What lifestyle factors and benefits and costs issues should...

Fly-Buy Frisbees sells a wide variety of frisbees and uses a perpetual inventory system. On June 1, Fly- Buy Frisbees had five Fast Flying Frisbees on hand at a unit cost of $105. During June and...

Fibertek, Inc., computed a pretax financial income of $40,000 for the first year of its operations ended December 31, 2013. Included in financial income was $25,000 of nondeductible expenses, $22,000...

(a) If Juan actually were well suited for sales, which work values and work-style factors do you think he would rate as very important? (b) What would you recommend to Juan regarding how to find out...

I - What should a project manager do if a stakeholder does not buy-in? What are the potential impacts if that were to happen? II - How should a project manager gain buy-in from stakeholders? What...

,.kindly solve please 1. Consider the simple regression model: V/i = Po+ Piri +ui, for i = 1, ..., n, with E(ur,) 7 0 and let z be a dummy instrumental variable for a, such that we can write: with...

1. Consider the production function Y, = AtK. L. "where A is total factor productivity (TFP), L is the labour force, and K is physical capital. Suppose TFP grows at 1% per year and a = 0.5 . If the...

i need help in 1.2 and 1.3 they both are related , In 1.3 you can read it off from 1.2 as the equations from 1.2 is needed in 1.3. 1.2 Random walks 1. Consider the simple random walk (e: is a...

1. Consider the simple random walk (et is a stationary white noise process) yt = yt1 + et Using back substitution (start with y1 = y0 + e1), rewrite the previous equation so that yt is a function of...

1. Consider a simple market with just five potential renters and four apartments. This table shows the maximum amount that each renter would be willing to pay for an apartment. The following graph...

1. Consider our "simple model of bid-ask spreads". Suppose that a dealer trades against an order which might come from an informed trader or a liquidity trader. The security's true value is either...