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Category: Differential Equation

Calculate-the-first-order-energy-correction-for-1-dimensional-non-degenerate-anharmonic-oscillator-whose-harmiltonian-is-HL-

Question Number 199996 by jlewis last updated on 12/Nov/23 $$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{first}\:\mathrm{order}\:\mathrm{energy}\:\mathrm{correction}\:\mathrm{for} \\ $$$$\mathrm{1}−\mathrm{dimensional}\:\mathrm{non}−\mathrm{degenerate}\:\mathrm{anharmonic} \\ $$$$\mathrm{oscillator}\:\mathrm{whose}\:\mathrm{harmiltonian}\:\mathrm{is}\:\mathscr{H}\underline{\mathscr{L}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

solve-the-associated-legendre-equation-l-l-1-2-l-0-1-2-and-m-2-l-l-1-which-requires-l-m-l-using-power-series-

Question Number 200022 by jlewis last updated on 12/Nov/23 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{associated}\:\mathrm{legendre}\:\mathrm{equation} \\ $$$$\lambda={l}\:\left({l}+\mathrm{1}\right)\eta^{\mathrm{2}} \:;{l}=\mathrm{0},\mathrm{1},\mathrm{2}…\:\:\:{and}\:{m}^{\mathrm{2}} \leqslant\:{l}\left({l}+\mathrm{1}\right)\: \\ $$$${which}\:{requires}\:−{l}\leqslant{m}\leqslant{l}\:\mathrm{using}\:\mathrm{power}\:\mathrm{series} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-198104

Question Number 198104 by sonu753 last updated on 10/Oct/23 Answered by mr W last updated on 11/Oct/23 $$\frac{{dx}}{{dy}}−\frac{{x}}{{y}}=−{y} \\ $$$$\left[{d}.{e}.\:{of}\:{type}\:{y}'+{p}\left({x}\right){y}={q}\left({x}\right)\right] \\ $$$$\int{p}\left({y}\right){dy}=−\int\frac{{dy}}{{y}}=−\mathrm{ln}\:{y} \\ $$$${u}\left({y}\right)={e}^{−\mathrm{ln}\:{y}} =\frac{\mathrm{1}}{{y}}…