By solving the Schrödinger equation, obtain the wave-functions for a particle of mass m in a...

By solving the Schrödinger equation, obtain the wave-functions for a particle of mass m in a one-dimensional “box” of length L

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genius_generous answered 2 years ago

Sketch the wave-function of the ground state of a particle of mass m which is con-...

Sketch the wave-function of the ground state of a particle of mass m which is con- fined in one dimension within a square potential well of infinite height, centred at x = 0 and of width a between x = ?a/2 and x = a/2. What type of function is that? If the infinite potential well is replaced by a potential well of finite height, sketch the new ground state wave-function. Explain qualitatively how the ground state energy changes in...

Consider a particle of mass ? in an infinite square well of width ?. Its wave...

Consider a particle of mass ? in an infinite square well of width ?. Its wave function at time t = 0 is a superposition of the third and fourth energy eigenstates as follows: ? (?, 0) = ? 3i?3(?)+ ?4(?) (Find A by normalizing ?(?, 0).) (Find ?(?, ?).) Find energy expectation value, <E> at time ? = 0. You should not need to evaluate any integrals. Is <E> time dependent? Use qualitative reasoning to justify. If you measure...

Derive the wave propagation equation for particle motion collinear with the direction of propagation. Assume a...

Derive the wave propagation equation for particle motion collinear with the direction of propagation. Assume a homogeneous, isotropic, linear-elastic, infinite, continuum medium. Follow your class notes, and clearly identify all assumptions made along the way. Then, assume the solution to the wave equation, i.e., the particle motion, replace into the differential equation and …. conclude!

Particle A of mass m, initial velocity 20i (m/s) has a collision with a stationary particle...

Particle A of mass m, initial velocity 20i (m/s) has a collision with a stationary particle B of mass 2m. After collision, VA(final)=10i+5j (m/s). a) Find VB(final) if the system (particle A plus B) linear momentum is conserved (both i and j directions). What are the velocities of center of the system before and after collision?b) Find the system’s % KE lost due to the collision (m=20.0gram). c) If the collision time between A and B is 0.050 s, what...

Using the minimal action principle obtain the equation of motion of the free particle from the...

Using the minimal action principle obtain the equation of motion of the free particle from the relativistic Lagrangian.

Consider a very small particle of mass, m, dropped in a fluid. The particle experiences a...

Consider a very small particle of mass, m, dropped in a fluid. The particle experiences a drag force, FD. The constant that relates the drag force to the velocity V is K. Determine the distance covered as the partcile accelerate from rest to 50 percent of its terminal velocity, Vt, in terms of K, m, and acceleration due to gravity, g.

The length of a simple pendulum is 0.75 m and the mass of the particle (the...

The length of a simple pendulum is 0.75 m and the mass of the particle (the “bob”) at the end of the cable is 0.26 kg. The pendulum is pulled away from its equilibrium position by an angle of 9.2° and released from rest. Assume that friction can be neglected and that the resulting oscillatory motion is simple harmonic motion. (a) What is the angular frequency of the motion? (b) Using the position of the bob at its lowest point...

The length of a simple pendulum is 0.80 m and the mass of the particle (the...

The length of a simple pendulum is 0.80 m and the mass of the particle (the “bob”) at the end of the cable is 0.31 kg. The pendulum is pulled away from its equilibrium position by an angle of 7.4° and released from rest. Assume that friction can be neglected and that the resulting oscillatory motion is simple harmonic motion. (a) What is the angular frequency of the motion? (b) Using the position of the bob at its lowest point...

The length of a simple pendulum is 0.78 m and the mass of the particle (the...

The length of a simple pendulum is 0.78 m and the mass of the particle (the "bob") at the end of the cable is 0.26 kg. The pendulum is pulled away from its equilibrium position by an angle of 8.70° and released from rest. Assume that friction can be neglected and that the resulting oscillatory motion is simple harmonic motion. (a) What is the angular frequency of the motion? ___rad/s (b) Using the position of the bob at its lowest...

A particle of mass m is constrained to a circle of radius r0: that is, the...

A particle of mass m is constrained to a circle of radius r0: that is, the potential for the particle is 0 when the particle is anywhere on that circle and infinite everywhere else, ?(?) = 0 (r=r0) V(r) = ∞ (? ≠ ?0) Find the eigenvalues and normalized eigenfunctions of the Hamiltonian for a particle on a ring. What is the degeneracy of eigenvalues for this system. how many eigenfunctions are there for each eigenvalue)?

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