AMATH 581 Autumn Quarter 2011
Homework 6: Bose-Einstein Condensation in 3D
DUE: Wednesday, December 7, 2011 (actually Thursday, 12/8 at 3 a.m.)
Consider the Gross-Pitaevskii system (nonlinear Schrodinger with potential) modeling a condensed
state of matte
AMATH 581 Autumn Quarter 2011
Homework 2: Quantum Harmonic Oscillator
DUE: Friday, October 21, 2011 (actually at 3am on 10/22)
Continuing on the idea of the harmonic oscillator of Homework 1:
(b) Calculate the rst ve normalized eigenfunctions (n ) and eig
AMATH 581
Practice 1: Autumn 2011
DUE: midnight, Thursday 10/6
I Consider the function
f (x) = x sin(3x) exp(x)
and solve for the x-value near x 0.5 that satises f (x) = 0. In the rst part, use
the Newton-Raphson method with the initial guess x(1) = 1.6 t
AMATH 581 Autumn Quarter 2016
Homework 2: Quantum Harmonic Oscillator
DUE: Friday, October 28, 2016 (actually at 3am on 10/29)
Continuing on the idea of the harmonic oscillator of Homework 1:
(b) Calculate the first five normalized eigenfunctions (n ) and
AMATH 581 Autumn Quarter 2016
Homework 4: Vorticity-Streamfunction Equations
DUE: Friday, November 11, 2016 (actually 3 a.m. on 11/12)
The time evolution of the vorticity (x, y, t) and streamfunction (x, y, t) are given by the governing equations:
t + [,
AMATH 581 Autumn Quarter 2016
Homework 5: Reaction-Diffusion Systems
DUE: Tuesday, November 22, 2016 (actually Wednesday, 11/23 at 3 a.m.)
Consider the reaction-diffusion system
Ut = (A)U (A)V + D1 2 U
Vt = (A)U + (A)V + D2 2 V
where A2 = U 2 + V 2 and 2
AMATH 581 Autumn Quarter 2016
Homework 1: Quantum Harmonic Oscillator
DUE: Friday, October 14, 2016 (actually at 3am on 10/15)
The probability density evolution in a one-dimensional harmonic trapping potential is governed by the partial
differential equat
AMATH 581 Autumn Quarter 2016
Homework 3: Vorticity-Streamfunction Equations
DUE: Friday, November 4, 2016 (actually at 3am on 11/5)
The time evolution of the vorticity (x, y, t) and streamfunction (x, y, t) are given by the governing equations:
t + [, ]
AMATH 581
Practice 1: Autumn 2016
DUE: midnight, Thursday 10/6
I Consider the function
f (x) = x sin(3x) exp(x)
and solve for the x-value near x 0.5 that satisfies f (x) = 0. In the first part, use
the Newton-Raphson method with the initial guess x(1) = 1
AMATH 581 Autumn Quarter 2016
Homework 6: Bose-Einstein Condensation in 3D
DUE: Wednesday, December 7, 2016 (actually Thursday, 12/8 at 3 a.m.)
Consider the Gross-Pitaevskii system (nonlinear Schrodinger with potential) modeling a condensed
state of matte