Difference between revisions of "Dynamically Shifted Oscillator"

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(→‎ξ0 = +1)
(→‎Lowest Eigenvalues)
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| Discretized Hamiltonian
 
| Discretized Hamiltonian
 
| 0.010
 
| 0.010
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| 1.500
−
|  
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| 3.037
−
|  
+
| 4.329
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| 5.603
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| 6.818
 
|-
 
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| Euler-Cromer  
 
| Euler-Cromer  

Revision as of 16:35, 2 June 2023


ξ0 = -1

DSOPotentialShiftMinusOne.png

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

DSOPotentialShiftPlusOne.png

Lowest Eigenvalues

Method Δx εi (ħω)
Discretized Hamiltonian 0.010 1.500 3.037 4.329 5.603 6.818
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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