Difference between revisions of "Dynamically Shifted Oscillator"

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==Lowest Eigenfunctions==
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{|border="1"
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! rowspan="2" | Method
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! colspan="5" | ''n''
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| 0
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| 1
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| 2
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| 3
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| 4
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| Discretized Hamiltonian
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| Euler-Cromer
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| [[File:DSOWaveFunctionShiftPlusOneEulerCromer0.png|200px]]
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| [[File:DSOWaveFunctionShiftPlusOneEulerCromer1.png|200px]]
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| [[File:DSOWaveFunctionShiftPlusOneEulerCromer2.png|200px]]
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| [[File:DSOWaveFunctionShiftPlusOneEulerCromer3.png|200px]]
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| --
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| Power Series
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Revision as of 15:50, 2 June 2023


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 DSOWaveFunctionDiscreteMatrix0.png DSOWaveFunctionDiscreteMatrix1.png DSOWaveFunctionDiscreteMatrix2.png DSOWaveFunctionDiscreteMatrix3.png DSOWaveFunctionDiscreteMatrix4.png
Euler-Cromer DSOWaveFunctionEulerCromer0.png DSOWaveFunctionEulerCromer1.png DSOWaveFunctionEulerCromer2.png DSOWaveFunctionEulerCromer3.png --
Power Series 200px 200px 200px 200px DSOWaveFunctionPowerSeries4.png

ξ0 = +1

Lowest Eigenvalues

Method Δx εi (ħω)
Discretized Hamiltonian 0.010
Euler-Cromer 0.010 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 DSOWaveFunctionShiftPlusOneEulerCromer0.png DSOWaveFunctionShiftPlusOneEulerCromer1.png DSOWaveFunctionShiftPlusOneEulerCromer2.png DSOWaveFunctionShiftPlusOneEulerCromer3.png --
Power Series
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