Solve for the motion of a free particle moving in one dimension with initial position and...

Solve for the motion of a free particle moving in one dimension with initial position and initial momentum using Hamilton –Jacobi theory. Please be sure to use the fact that the resulting Kamiltonian vanishes to simplify your work. Comment on the results you find.

Expert Solution

genius_generous answered 2 years ago

A particle with mass m and energy E is moving in one-dimension from right to legt....

A particle with mass m and energy E is moving in one-dimension from right to legt. It is incident on the step potential V(x)=0 for x<0 nd V(x)=V0 for x>0 where E>V0>0. Find the reflection coefficient R in terms of m,E and V0, and h-bar.

Particle Position and Time The position of a particle moving along the x axis depends on...

Particle Position and Time The position of a particle moving along the x axis depends on the time according to the equation x = ct2 - bt3, where x is in meters and t in seconds. (a) What dimension and units must c have? s2/ms/m2 m/s2m2/s What dimension and units must b have? m3/ss/m3 s3/mm/s3 For the following, let the numerical values of c and b be 3.3 and 1.0 respectively. (b) At what time does the particle reach its maximum positive...

A particle is moving with the given data. Find the position of the particle. a(t) =...

A particle is moving with the given data. Find the position of the particle. a(t) = 11 sin(t) + 3 cos(t), s(0) = 0, s(2π) = 18

A particle is moving with the given data. Find the position of the particle. v(t) =...

A particle is moving with the given data. Find the position of the particle. v(t) = sin(t) − cos(t), s(0) = 4

3) The momentum eigenfunction for a particle moving in one dimension is фр--h-1/2eipz/n The energy eigenfunction...

3) The momentum eigenfunction for a particle moving in one dimension is фр--h-1/2eipz/n The energy eigenfunction for a particle in a 1D box of length L is u()- is expanded in terms of фе(x), the expansion coefficient may be interpreted as the momentum probability amplitude; its square gives the probability density for momentum. Determine the momentum probability density for u(x)

1. A particle is moving with the given data. Find the position of the particle. a(t)=2t+7,...

1. A particle is moving with the given data. Find the position of the particle. a(t)=2t+7, s(0)=8, v(0)=-3 2.Find f f'(x)=1 sqrt(1-x2) , f(1/2)=8

Two objects, moving in one dimension, undergo an isolated collision. Object A has initial velocity 1...

Two objects, moving in one dimension, undergo an isolated collision. Object A has initial velocity 1 m/s. Object B has an initial velocity -3 m/s. After the collision, the relative velocity of the two objects is vAB=+2 m/s. The reduced mass of the two objects is ⅔ kg. What is the change in total kinetic energy of the entire system during this collision? (If it decreases, make your answer negative.) Express your answer in units of Joules, but enter only...

A sensor uses ultrasound to measure position and velocity of a moving cart in 1 dimension.

A sensor uses ultrasound to measure position and velocity of a moving cart in 1 dimension. It emits acoustic waves at 25 kHz and the speed of sound in air is 343 m/s. The maximum range of the cart from the wave emitter is 3 meters.A: If the sensor wants to measure distance position accurately to within 1cm of the cart, what is the maximum velocity the cart can have and not change position by more than 1cm while the...

write parametric equations in 2D for a particle moving in a clockwise motion along a circle...

write parametric equations in 2D for a particle moving in a clockwise motion along a circle radius 2 such that at t=0 , the particle is at point (-2,0) Please I need the answer with steps and explanation.. Clear handwriting please.. Thank you

The position of a particle moving along the x axis depends on the time according to...

The position of a particle moving along the x axis depends on the time according to the equation x = ct2 - bt3, where x is in meters and t in seconds. For the following, let the numerical values of a and b be 3.7 and 1.0 respectively. a) At what time does the particle reach its maximum positive x position? b) What distance does the particle cover in the first 4.0s? c) What is its displacement from t=0s to...

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