View source for Dynamically Shifted Oscillator

= Varying ξ<sub>0</sub> =
==Lowest Eigenvalues ==
=== ξ<sub>0</sub> < 0 ===
[[File:DSOLowestFiveEigenvaluesVaryingNegativeShifts.png|400px]]

==Lowest Eigenfunctions ==
=== ξ<sub>0</sub> < 0 ===
[[File:DSOLowestEigenvalueEigenfunctionVaryingNegativeShifts.png|400px]]

= ξ<sub>0</sub> = -1 =
[[File:DSOPotentialShiftMinusOne.png|400px]]
== Lowest Eigenvalues ==

{|border="1"
! Method
! Δ''x''
! colspan="5" | ''ε''<sub>''i''</sub> (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==

{|border="1"
! rowspan="2" | Method
! colspan="5" | ''n'' 
|-
| 0
| 1
| 2
| 3
| 4
|-
| Discretized Hamiltonian
| [[File:DSOWaveFunctionDiscreteMatrix0.png|200px]]
| [[File:DSOWaveFunctionDiscreteMatrix1.png|200px]]
| [[File:DSOWaveFunctionDiscreteMatrix2.png|200px]]
| [[File:DSOWaveFunctionDiscreteMatrix3.png|200px]]
| [[File:DSOWaveFunctionDiscreteMatrix4.png|200px]]
|- 
| Euler-Cromer
| [[File:DSOWaveFunctionEulerCromer0.png|200px]]
| [[File:DSOWaveFunctionEulerCromer1.png|200px]]
| [[File:DSOWaveFunctionEulerCromer2.png|200px]]
| [[File:DSOWaveFunctionEulerCromer3.png|200px]]
| --
|-
| Power Series
| [[File:DSOWaveFunctionPowerSeries0.png|200px]]
| [[File:DSOWaveFunctionPowerSeries1.png|200px]]
| [[File:DSOWaveFunctionPowerSeries2.png|200px]]
| [[File:DSOWaveFunctionPowerSeries3.png|200px]]
| [[File:DSOWaveFunctionPowerSeries4.png|200px]]
|}

= ξ<sub>0</sub> = +1 =
[[File:DSOPotentialShiftPlusOne.png|400px]]

== Lowest Eigenvalues ==

{|border="1"
! Method
! Δ''x''
! colspan="5" | ''ε''<sub>''i''</sub> (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==

{|border="1"
! rowspan="2" | Method
! colspan="5" | ''n'' 
|-
| 0
| 1
| 2
| 3
| 4
|-
| Discretized Hamiltonian
| [[File:DSOWaveFunctionShiftPlusOneDiscreteMatrix0.png|200px]]
| [[File:DSOWaveFunctionShiftPlusOneDiscreteMatrix1.png|200px]]
| [[File:DSOWaveFunctionShiftPlusOneDiscreteMatrix2.png|200px]]
| [[File:DSOWaveFunctionShiftPlusOneDiscreteMatrix3.png|200px]]
| [[File:DSOWaveFunctionShiftPlusOneDiscreteMatrix4.png|200px]]
|- 
| Euler-Cromer
| [[File:DSOWaveFunctionShiftPlusOneEulerCromer0.png|200px]]
| [[File:DSOWaveFunctionShiftPlusOneEulerCromer1.png|200px]]
| [[File:DSOWaveFunctionShiftPlusOneEulerCromer2.png|200px]]
| [[File:DSOWaveFunctionShiftPlusOneEulerCromer3.png|200px]]
| --
|-
| Power Series
|
| -
|
|
|
|}