Solve schroedinger's equation for a three dimensional harmonic
oscillator and obtain its eigen values and eigen functions.Are the
energy levels degenerate? Explain what is the minimum uncertainty
in its location in the lowest state.
Separate the wave equation in two-dimensional rectangular
coordinates x, y. Consider a rectangular membrane, rigidly attache
to supports along its sides, such that a ≤ x ≤ 0 and b ≤ y ≤ 0.
Find the solution, including the specification of the
characteristic frequencies of the membrane oscillations. In the
case of a = b, show that two or more modes of vibration correspond
to a single frequency
Consider a particle that is free (U=0) to move in a
two-dimensional space. Using polar coordinates as generalized
coordinates, solve the differential equation for rho and
demonstrate that the trajectory is a straight line.
The spiral of Archimedes is a curve described in polar
coordinates by the equation ?? = ???? where ?? is the distance of a
point from the origin, and ?? is the angle of the point in radians
with respect to the positive x-axis. Write an m-file to create a
plot of the spiral of Archimedes using 1000 points for 0 ? ?? ? 6??
?????? when k = 0.5. Be sure to include a title, axis labels, and
grid...
1. Show an engineering problem and solve the kinematic
parameters by using polar coordinates systems used
to define the motion of an object.
Note: Provide a clear diagram of the suggested engineering problem
with detailed calculation.
Solve the following problem using the simplex method. If the
problem is two dimensional, graph the feasible region, and outline
the progress of the algorithm.
Max
Z = 5X1 + 3X2 +
2X3
Subject to 4X1 + 5X2 +
2X3 + X4≤ 20
3X1 + 4X2 - X3 + X4≤ 30
X1, X2, X3, X4 ≥
0
1)
a) Establish schrodinger equation,for a linear harmonic
oscillator and solve it to obtain its eigen values and eigen
functions.
b) calculate the probability of finding a simple harmonic
oscillator within the classical limits if the oscillator in its
normal state.