Dynamically Shifted Oscillator

Varying ξ₀

Lowest Eigenvalues

ξ₀ < 0

ξ₀ > 0

Lowest Eigenfunctions

ξ₀ < 0

ξ₀ > 0

ξ₀ = -1

Lowest Eigenvalues

Method	Δx	εi (ħω)
Discretized Hamiltonian	0.010	0.3095	0.7342	1.5000	2.1974	2.9987
Euler-Cromer	0.001	0.3095	0.734	1.4997	2.197
Runge-Kutta 45	0.010			1.496		3.037

Lowest Eigenfunctions

Method	n
	0	1	2	3	4
Discretized Hamiltonian
Euler-Cromer					--
Power Series	200px	200px	200px	200px

ξ₀ = +1

Lowest Eigenvalues

Method	Δx	εi (ħω)
Discretized Hamiltonian	0.001	1.500	3.037	4.329	5.604	6.818
Euler-Cromer	0.001	1.499	3.038	4.328	5.60
Runge-Kutta 45	0.010

Lowest Eigenfunctions

Method	n
	0	1	2	3	4
Discretized Hamiltonian
Euler-Cromer					--
Power Series		-