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1
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Analytical approach calculating eigenfrequencies and modes of stator cores in AC machines

100%
Witczak P.
|
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vol. 61
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issue 1
2
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Physics-guided neural networks (PGNNs) to solve differential equations for spatial analysis

88%
Borzyszkowski B., Damaszke K., Romankiewicz J., Świniarski M., Moszyński M., Borzyszkowski B., Damaszke K., Romankiewicz J., Świniarski M., Moszyński M.
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2021
3
Content available remote

Exact and approximate solutions to Schrödinger’s equation with decatic potentials

75%
Brandon D., Saad N.
Open Physics
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2013
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vol. 11
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issue 3
279-290
EN
The one-dimensional Schrödinger’s equation is analysed with regard to the existence of exact solutions for decatic polynomial potentials. Under certain conditions on the potential’s parameters, we show that the decatic polynomial potential V (x) = ax 10 + bx 8 + cx 6 + dx 4 + ex 2, a > 0 is exactly solvable. By examining the polynomial solutions of certain linear differential equations with polynomial coefficients, the necessary and sufficient conditions for corresponding energy-dependent polynomial solutions are given in detail. It is also shown that these polynomials satisfy a four-term recurrence relation, whose real roots are the exact energy eigenvalues. Further, it is shown that these polynomials generate the eigenfunction solutions of the corresponding Schrödinger equation. Further analysis for arbitrary values of the potential parameters using the asymptotic iteration method is also presented.
4
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Explicit commutativity conditions for second-order linear time-varying systems with non-zero initial conditions

75%
Koksal M. E., Koksal M. E.
Archives of Control Sciences
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2019
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vol. 29
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issue 3
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