Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential

Table 2

Conditions on the value of the parameters 𝑔 and 𝜇 for the quasipolynomial solutions in the case of Δ₂=0 with different values of 𝑤𝑎² and 𝑙.

𝑛	𝑙	𝑤𝑎^2	Conditions	𝐸^𝑤𝑎2𝑛,𝑙≡𝐸^𝑤𝑎2𝑛,𝑙(𝜇,𝑔)
	0	3/2	𝜇=−11/3+𝐵	𝐸^3/21,0=−1/6(35−12𝐵)𝑤
			𝑔=(−14/3+𝐵)(−17/3+𝐵)
			𝐵=1/3ℜ(𝐴^1/3+43𝐴^−1/3),𝐴=−98+9𝑖√863
			𝜇=−11/3−𝐵,	𝐸^11,0=−1/6(35+12𝐵)𝑤
			𝑔=1/9(17+3𝐵)(14+3𝐵)
			𝐵=1/6ℜ(43(1+𝑖√3)𝐴^−1/3+(1−𝑖√3)𝐴^1/3),𝐴=−98+9𝑖√863
			𝜇=−11/3−𝐵,	𝐸^11,0=−1/6(35+12𝐵)𝑤
			𝑔=1/9(17+3𝐵)(14+3𝐵)
			𝐵=1/6ℜ(43(1−𝑖√3)𝐴^−1/3+(1+𝑖√3)𝐴^1/3),𝐴=−98+9𝑖√863
		2	𝜇=−13/3+𝐵	𝐸^3/21,0=−1/6(43−12𝐵)𝑤
			𝑔=1/9(−16+3𝐵)(−19+3𝐵)
			𝐵=1/3ℜ(𝐴^1/3+55𝐴^−1/3),𝐴=−55+165𝑖√6
			𝜇=−13/3−𝐵,	𝐸^11,0=−1/6(43+12𝐵)𝑤
			𝑔=1/9(16+3𝐵)(19+3𝐵)
			𝐵=1/6ℜ(55(1+𝑖√3)𝐴^−1/3+(1−𝑖√3)𝐴^1/3),𝐴=−55+165𝑖√6
			𝜇=−13/3−𝐵,	𝐸^11,0=−1/6(43+12𝐵)𝑤
			𝑔=1/9(16+3𝐵)(19+3𝐵)
			𝐵=1/6ℜ(55(1−𝑖√3)𝐴^−1/3+(1+𝑖√3)𝐴^1/3),𝐴=−55+165𝑖√6