Dirac Particle for the Position Dependent Mass in the Generalized Asymmetric Woods-Saxon Potential

Table 1

The special potentials: the symmetric potentials and asymmetric (asy.) potentials (pot.).

The GAWSp	The asy. Hulthen pot.	The asy. cusp pot.
𝑉(𝑥)=𝑉0𝜃(−𝑥)𝑞+𝑝𝑒^−𝑎(𝑥+𝐿)+𝜃(𝑥)𝑞+𝑝𝑒^𝑏(𝑥−𝐿)	𝑞⟶−𝑞, 𝑞⟶−𝑞	𝐿=𝐿=0,
	𝐿=𝐿=0, 𝑝=𝑝=1,	𝑞=𝑞=0, 𝑝=𝑝=1,
	𝑉(𝑥)=𝑉0𝜃(−𝑥)𝑒^−𝑎𝑥+−𝑞𝜃(𝑥)𝑒^𝑏𝑥−𝑞	𝑉(𝑥)=𝑉0𝜃(−𝑥)𝑒^−𝑎𝑥+𝜃(𝑥)𝑒^𝑏𝑥
The Woods-Saxon pot.	The Hulthen pot.	The cusp pot.
𝑎=𝑏, 𝐿=𝐿,	𝑎=𝑏, 𝑞⟶−𝑞, 𝑞⟶−𝑞	𝑎=𝑏, 𝐿=𝐿=0,
𝑞=𝑞=1, 𝑝=𝑝=1,	𝐿=𝐿=0, 𝑝=𝑝=1,	𝑞=𝑞=0, 𝑝=𝑝=1,
𝑉(𝑥)=𝑉0𝜃(−𝑥)1+𝑒^−𝑎(𝑥+𝐿)+𝜃(𝑥)1+𝑒^𝑎(𝑥−𝐿)	𝑉(𝑥)=𝑉0𝜃(−𝑥)𝑒^−𝑎𝑥+−𝑞𝜃(𝑥)𝑒^𝑎𝑥−𝑞	𝑉(𝑥)=𝑉0𝜃(−𝑥)𝑒^−𝑎𝑥+𝜃(𝑥)𝑒^𝑎𝑥