Quantum Mechanics Answers

Calculate the momentum of a proton whose kinetic energy is 200 MeV.

Calculate the kinetic energy of a proton whose velocity is 0.8c.

Hypervelocity bullet used in 0.22 long rifle usually weigh around 2.1 g and can have a speed of 550 m/s. what must be the speed of a 75 kg man to match the momentum of this bullet?

Fermions and Bosons There is a fundamental difference between fermions and bosons which is responsible for the construction eigenstates of atoms with several electrons. Here we study a very simple case. For a single particle with mass m in a one-dimensional box-potential a < x < a, the energy eigenvalues are En = E1 *n^2, n = 1, 2 ,3, with E1=hbar^2pi^2/(8ma^2) and corresponding eigenfunctions φn(x).

Consider now the ground state for three identical non-interacting spinless particles with coordinates x1, x2, and x3, respectively.

(a) What are the symmetry properties of the ground state wavefunctions φg for bosons or fermions? Express these properties for the three-particle wavefunction φg(x1,x2,x3).

(b) Write down the values of ground state energy Eg for bosons and fermions.

(c) Write down the ground state wavefunction φg(x1,x2,x3) for bosons and fermions.

Fermions and Bosons There is a fundamental difference between fermions and bosons which is responsible for the construction eigenstates of atoms with several electrons. Here we study a very simple case. For a single particle with mass m in a one-dimensional box-potential a < x < a, the energy eigenvalues are En = E1 *n^2, n = 1, 2 ,3, with E1=hbar^2pi^2/(8ma^2) and corresponding eigenfunctions φn(x).

Consider now the ground state for three identical non-interacting spinless particles with coordinates x1, x2, and x3, respectively.

(a) What are the symmetry properties of the ground state wavefunctions φg for bosons or fermions? Express these properties for the three-particle wavefunction φg(x1,x2,x3).

(b) Write down the values of ground state energy Eg for bosons and fermions.

(c) Write down the ground state wavefunction φg(x1,x2,x3) for bosons and fermions.

 Now use spherical coordinates, in which r2 = x2 + y2 + z2 and thus the oscillator potential is V(r) = 1/ 2 m omega^2^R^2. Again carry out a separation of variables, but now use spherical coordinates,  ψ n l m (r, θ, φ) = 1/r U(r)n l Y l m (θ, φ), (7) Derive the eigenvalue differential equations for the u(r), and also for the Y lm. You are not supposed to solve the radial equation for the u’s!

the normalized wave function for the first excited state of particle in one dimensional box

You're rolling solid rubber balls on the kitchen floor. Ball 1 has a density of 1.00 ×

×10

3

3kg/m

3

kg/m3and a radius of 30.0 mm

mm . Ball 2 has an unknown density and a radius of 43.0 mm

mm and is initially at rest. You roll ball 1 at an initial speed of 3.00 m/s

m/s, and the two balls collide head-on. Ball 1 reverses direction and comes back to you at 2.00 m/s

m/s, and after the collision, the speed of ball 2 is 1.00 m/s

m/s. The positive x

x axis is in the direction of ball 1's initial motion. 1.What is the initial momentum of ball 2.

2 what is the density of ball 2

3. What is the initial momentum of ball 1

Consider an infinitely deep potential well of width 2a centered at x = 0.

The probability of finding a particle of mass m in the ground, first and

second excited state is 60%, 30% and 10% respectively. What is the energy

expectation value of the particle ?

What is quantum dot