Consider a classical harmonic oscillator of mass m and spring constant k . What is the...

Consider a classical harmonic oscillator of mass

and spring constant

. What is the probability

density for finding the particle at position

? How does this compare to the probability density for

the ground state of a quantum mechanical harmonic oscillator

Solutions

Expert Solution

I have done detailed analysis of classical harmonic oscillator and little less of quantum harmonic oscillator but I worked out all the details

Please UpVote and let me know if you face any problem, confusion or see any error.
I will get back to you asap.

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A H2 molecule can be approximated by a simple harmonic oscillator having a spring constant k...

A H2 molecule can be approximated by a simple harmonic oscillator having a spring constant k = 1.1 ✕ 103 N/m. (a) How many different energy transitions are possible when the H2 molecule decays from the third excited state down to the ground state? (b) Find the photon energies produced in these transitions and their wavelengths. Enter 0 in any unused boxes. relative energy transition energy wavelengths lowest eV nm middle eV nm highest eV...

Consider the undamped forced harmonic oscillator with mass 1 kg, damping coefficient 0, spring constant 4,...

Consider the undamped forced harmonic oscillator with mass 1 kg, damping coefficient 0, spring constant 4, and external force h(t) = 3cos(t). The mass is initially at rest in the equilibrium position. You must understand that you can model this as: y’’ = -4y +3cost; y(0) = 0; y’(0) = 0. (5pts) Using the method of Laplace transforms, solve this initial value problem. Check your solution solves the IVP. (4pts) Be sure to check that your solution satisfies both the...

(10pts) Consider the damped forced harmonic oscillator with mass 1 kg, damping coefficient 2, spring constant...

(10pts) Consider the damped forced harmonic oscillator with mass 1 kg, damping coefficient 2, spring constant 3, and external force in the form of an instantaneous hammer strike (Section 6.4) at time t = 4 seconds. The mass is initially displaced 2 meters in the positive direction and an initial velocity of 1 m/s is applied. Model this situation with an initial value problem and solve it using the method of Laplace transforms.

Consider a mass spring system. The spring has a constant k=30N/m and mass=3kg. The mass oscillates...

Consider a mass spring system. The spring has a constant k=30N/m and mass=3kg. The mass oscillates w/amplitude of 10cm. a.)what is the frequency of oscillation b.) what is the displacement at time t=0 c.) when is the first time the mass is at maximum displacement? (t=?) d.) what is the maximum acceleration felt by the mass? Where in the motion does this occur? e.)what is the minimum acceleration felt by the mass? Where in the motion does this occur? f.)What...

A particle of mass m is attached to a spring with a spring constant k. The...

A particle of mass m is attached to a spring with a spring constant k. The other end of the spring is forced to move in a circle in the x ? y plane of radius R and angular frequency ?. The particle itself can move in all 3 directions. Write down the Lagrangian, and derive the equations of motion.

consider a linearly damped simple harmonic oscillator with mass m,restoring force contsant k and resistive force...

consider a linearly damped simple harmonic oscillator with mass m,restoring force contsant k and resistive force constant c.if c >sqrt(4mk), work out the expression for the displacement as a function of time and describe the predicted time dependence of the motion.

The displacement as a function of time of a 4.0kg mass spring simple harmonic oscillator is...

The displacement as a function of time of a 4.0kg mass spring simple harmonic oscillator is . What is the displacement of the mass at 2.2 seconds? ___________m What is the spring constant? ___________________N/m What is the position of the object when the speed is maximum? ______________m What is the magnitude of the maximum velocity?____________________m/s

A simple harmonic oscillator consists of a 0.63 kg block attached to a spring (k =...

A simple harmonic oscillator consists of a 0.63 kg block attached to a spring (k = 190 N/m). The block slides on a horizontal frictionless surface about the equilibrium point x = 0 with a total mechanical energy of 6.0 J. (a) What is the amplitude of the oscillation? (b) How many oscillations does the block complete in 12 s? (c) What is the maximum kinetic energy attained by the block? (d) What is the speed of the block at...

1. A block of mass m attached to a spring with spring constant k oscillates horizontally...

1. A block of mass m attached to a spring with spring constant k oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x = -5 cm. Taking m = 100 gm, and spring constant = 2.5 N/m, a) Find out the equations of position, velocity, and acceleration of the ball. Find also the total energy of the block when its velocity was 20 cm/s. b) Oscillating particles generate waves. What will be the equation of a...

A simple harmonic oscillator consists of a block of mass 3.70 kg attached to a spring...

A simple harmonic oscillator consists of a block of mass 3.70 kg attached to a spring of spring constant 260 N/m. When t = 1.60 s, the position and velocity of the block are x = 0.199 m and v = 3.920 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?

Subjects