Timeline for Spectral growth of One dimensional Schrodinger Operator
Current License: CC BY-SA 3.0
12 events
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| Mar 20, 2017 at 18:47 | comment | added | Surajit | Thanks you very much for the details.Now it is clear to me. | |
| Mar 20, 2017 at 18:44 | vote | accept | Surajit | ||
| Mar 20, 2017 at 14:26 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
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| Mar 20, 2017 at 14:05 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
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| Mar 20, 2017 at 14:05 | comment | added | Alexandre Eremenko | Whether $a$ is positive or negative, does not matter for asymptotics of (very large) eigenvalues. For the rate of growth look in the paper of Shin, for example. | |
| Mar 20, 2017 at 6:47 | comment | added | Surajit | In the Potential function $V$ ,$a$(the coefficient of $x^2$) can be highly negative as well,so in that case the differential equation you took would be of the form $-y''+(x^4+ax^2)y=\lambda y$,So,I really wanted to know the singular value distribution of this differential equation for $|a|$ large enough.Could you please help me on that?Also,in the paper 'C. Bender and T. Wu, Anharmonic oscillator. Phys. Rev. (2) 184 1969 1231–1260',I think they gave some asymptotic expansion of the Ground state energy.So,could you elaborate more about the growth $\lambda_n\sim cn^{4/3}$? | |
| Mar 18, 2017 at 15:58 | vote | accept | Surajit | ||
| Mar 20, 2017 at 6:52 | |||||
| Mar 18, 2017 at 15:15 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
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| Mar 18, 2017 at 15:09 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
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| Mar 18, 2017 at 15:03 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
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| Mar 18, 2017 at 14:52 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
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| Mar 18, 2017 at 14:42 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |