For the some unknown Hamiltonian, we will use a trial wave function ?? = ??₁??₁ + ??₂??₂ . Where ??1 ?????? ??2 are known functions

a. What are the variational parameters of this trial wave function (2 points)?

b. Minimizing the average energy will lead to a secular Determinant.Write down an expression for the Secular Determinant for this system using the following symbols (4 points)

??_11, ??₁₂ = ??_21, ??₂₂, ??_11, ??₁₂ = ??_21, ??_22, E.

c. Write a mathematical expression using ??₁, ??₂, and any necessary operators to define (2 points)

??₂₂=

??₂₁=

Two resistors of exactly the same resistance are hooked in series to a power supply and the total current: I_tot(series) is measured. The same two resistors are then connected to the same power supply in parallel. The total parallel current is related to the total series current through the relationship:

Select one:

a. I_tot(parallel) = 1/4 × I_tot(series)

b. I_tot(parallel) = 1/2 × I_tot(series)

c. I_tot(parallel) = 2 × I_tot(series)

d. I_tot(parallel) = 8 × I_tot(series)

e. I_tot(parallel) = 1/8 × I_tot(series)

f. I_tot(parallel) = 4 × I_tot(series)

g. I_tot(parallel) = I_tot(series)

2. a)

A 0.20 kg hockey puck on a frictionless surface is hit with a stick. The force of the stick on the puck, during the 0.4 seconds while they are in contact, causes the puck to go from rest to 36 meters per second east. What was the magnitude of the average force of the stick on the puck while they were in contact?

b)

A 3-kg block is placed on a frictionless ramp-incline, where it slides from rest, 18 m down along the ramp- incline in 4 seconds.

What was the angle of the incline, with respect to the horizontal?

The position of a particle moving along an x axis is given by x = 12.0t2 - 4.00t3, where x is in meters and t is in seconds. Determine (a) the position, (b) the velocity, and (c) the acceleration of the particle at t = 5.00 s. (d) What is the maximum positive coordinate reached by the particle and (e) at what time is it reached? (f) What is the maximum positive velocity reached by the particle and (g) at what time is it reached? (h) What is the acceleration of the particle at the instant the particle is not moving (other than at t = 0)? (i) Determine the average velocity of the particle between t = 0 and t = 5.00 s.

From atomic mass and density, estimate the lattice constants of Si, Ge, GaAs, InAs, and InSb. (I'm having trouble with the GaAs, InAs and InSb).

-Discuss three real-life quantities that are naturally described by complex numbers. Show that by mathematical equations.
-In A.C. circuit what does real part of the circuit present? And, what does the imaginary part present?
_Through explaining different forms of complex numbers show which for present a position vector.
-How does Laplace Transform relate to the complex plane?
-Complex functions used to describe Potential Flow in two dimensions in fluid dynamics.

Suppose that 132 moles of a monatomic ideal gas is initially contained in a piston with a volume of 0.94 m³at a temperature of 348 K. The piston is connected to a hot reservoir with a temperature of 1064 K and a cold reservoir with a temperature of 348 K. The gas undergoes a quasi-static Stirling cycle with the following steps:

1. The temperature of the gas is increased to 1064 K while maintaining a constant volume.
2. The volume of the gas is increased to 3.38 m³ while maintaining a constant temperature.
3. The temperature of the gas is decreased to 348 K while maintaining a constant volume.
4. The volume of the gas is decreased to 0.94 m³ while maintaining a constant temperature.

It may help you to recall that CV = 12.47 J/K/mole for a monatomic ideal gas, and that the number of gas molecules is equal to Avagadros number (6.022

A) A 46.1 kg girl is standing on a 169 kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.61 m/s relative to the plank. What is her velocity relative to the ice surface?

B) What is the velocity of the plank relative to the ice surface?

(a) Explain briefly what is meant by atmospheric pressure, and why it decreases with altitude.

(b) Explain the role of the Earth’s magnetosphere in protecting the atmosphere from solar wind, and in creating the auroras.

(c) Why is the sky blue? Would you expect to see blue skies on other planets?

Write an example "background" information for exponential decay using beer froth experiment:

Do the rays reflected from the plane mirror obey the Law of Reflection? Explain.

Humans have little or no sensitivity to polarized light, and no sensitivity at all to ultraviolet light while many invertebrates such as insects do. In what way do you think this would be useful to an organism?

In words, but making use of equations where appropriate, explain how the Principal of Conservation of Linear Momentum is a demonstration of Newton’s third law of motion. In particular, consider a simple collision between two objects. The collision may be either elastic or inelastic. It may be head-on or oblique. State how the changes in motion as a result of this collision relate to Newton’s Third Law. Finally expand your reasoning to cover a many particle system.