Title:
Tutorial example - 2d harmonic oscillator
The purpose of this exercise is to
(1) understand how to specify a 2-dimensional problem
(2) see the onset of the "curse of dimension" already here
[TASK] vary the Axis and see what happens
# Below we define our discretization axis:
Axis: name,nCoefficients,lower end, upper end,functions,order
X1,24,-7,7,polynomial,12
X2,32,-7,7,polynomial,8
# NOTE: the axes need not be identical,
# although, of course, there is no good reason to have them different in this example
# NOTE: the coordinate type (here: X) can be numbered
# alternatively, we could specify
# X,24,-7,7,polynomial,12
# Y,32,-7,7,polynomial,8
# or any combination of these
# Hamiltonian in the tensor product space L2( dx1 dx2, R^2) = L2(dx1,R) (x) L2(dx2,R)
Operator: hamiltonian
0.5(<1>+<1>)+0.5<1>+0.5<1>
# NOTE: what we usually denote as d^2/dx^2 + d^2/dy^2 is, mathematically speaking
# a tensor product d^2/(x^2 (x) 1 + 1 (x) d^2/dy^2
# this is the principle for the notation of operators in tRecX
# we will print the lowest eigenvalues and stop
Eigen: select=SmallReal[20]