Shape-invariance approach and Hamiltonian hierarchy method on the Woods–Saxon potential for ℓ ≠ 0 states

An analytically solvable Woods–Saxon potential for ℓ ≠ 0 states is presented within the framework of Supersymmetric Quantum Mechanics formalism. The shape-invariance approach and Hamiltonian hierarchy method are included in calculations by means of a translation of parameters. The approximate energy spectrum of this potential is obtained for ℓ ≠ 0 states, applying the Woods–Saxon square approximation to the centrifugal barrier term of the Schrödinger equation.