Difference between revisions of "Dynamically Shifted Oscillator"
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=== ξ<sub>0</sub> < 0 === | === ξ<sub>0</sub> < 0 === | ||
[[File:DSOLowestFiveEigenvaluesVaryingNegativeShifts.png|400px]] | [[File:DSOLowestFiveEigenvaluesVaryingNegativeShifts.png|400px]] | ||
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| + | === ξ<sub>0</sub> > 0 === | ||
| + | [[File:DSOLowestFiveEigenvaluesVaryingPositiveShifts.png|400px]] | ||
==Lowest Eigenfunctions == | ==Lowest Eigenfunctions == | ||
Latest revision as of 09:52, 23 July 2023
Contents
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 | 
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| Euler-Cromer | 
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| Power Series | 200px | 200px | 200px | 200px | 
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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 | 
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| Euler-Cromer | 
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| Power Series | - | ||||
