In: Physics

Consider a two level system interacting with a radiation field.
Write down the differential equations defining the Einstein
**A** and **B** coefficients.
*Define all terms in your equations.*

a. Solve for the time varying upper state population density for the case of no external radiation present.

b. In steady state, solve for the photon energy density.

c. What other concept is required to predict the possibility of laser action?

Write the second order differential equation as a system of two
linear differential equations then solve it.
y" + y' - 6y = e^-3t y(0) =0 y'(0)=0

Write down your own verbal description for a dynamical system,
and write down the equations for the dynamical system. (It is fine
if this system is very simple! It is also fine if the scenario is
not very realistic, as long as the equations match the
description!)

Write down an augmented matrix in reduced form corresponding to
a system with 3 equations and 5 variables which has infinitely many
solutions and 2 free variables.
Write down an augmented matrix in reduced form corresponding to
a system with 4 equations and 5 variables which has no solutions
and 2 free variables.

Write down Maxwell’s Equations (integral notation). Write down a
modified version of Maxwell’s Equations that includes magnetic
monopoles. Use the symbol qm for magnetic change and J for magnetic
current. Hint: Think of symmetry and units.

Solve the given system of differential equations. ??/?? = ? + 4?
??/?? = ? + y

Write down three examples on homogeneous linear second order
differential equations and put them into self-adjoint form.

Write down three examples on homogeneous linear second order
differential equations and put them into self-adjoint form.

A system of differential equations solved by the Laplace
transform has led to the following system:
(s-3) X(s) +6Y(s) = 3/s
X(s) + (s-8)Y(s) = 0
Obtain the subsidiary equations and then apply the inverse
transform to determine x (1)

Report about (Applications of Differential Equations in Heat Exchanger System)

Write the four Maxwell’s Equations, together with the defining
relationship for the fields (F~ = q(E~ + ~v × B~ ), and give a
short summary of the experimental basis for each and define all
symbols. Then describe Maxwell’s modification of Ampere’s Law and
outline (without mathematical details) how it shows that light is
an electromagnetic wave.

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