S𝔻$g=(Sqrt[((Cosh[(ℏ/2)(Sqrt[(t^2)+(γ^2) (ϵ^2)+4 ϵ ϖ])]-Cosh[((ℏ t-ℏ ϵ γ)/2)-a ϵ ℏ])/(Sinh[((γ ϵ ℏ)/2)](t (2 a+γ)-2 a (a+γ) ϵ+2 ϖ) ℏ/(2γ)))]);
S𝔻$g=(Sqrt[((Cosh[(ℏ/2)(Sqrt[(t^2)+(γ^2) (ϵ^2)+4 ϵ ϖ])]-Cosh[((ℏ t)/2)-a ϵ ℏ-((γ ϵ ℏ)/2)])/(Sinh[((γ ϵ ℏ)/2)](t (2 a+γ)-2 a (a+γ) ϵ+2 ϖ) ℏ/(2γ)))]);
S𝔻$g=(Sqrt[((Cosh[(ℏ/2)(Sqrt[(t^2)+(γ^2) (ϵ^2)+4 ϵ ϖ])]-Cosh[(ℏ/2)(t-2 a ϵ-γ ϵ)])/(Sinh[((γ ϵ ℏ)/2)](t (2 a+γ)-2 a (a+γ) ϵ+2 ϖ) ℏ/(2γ)))]);
S𝔻$g=(Sqrt[((Cosh[(ℏ/2)(Sqrt[(t^2)+(γ^2) (ϵ^2)+4 ϵ ϖ])]-Cosh[(ℏ/2)(t-(2 a+γ) ϵ)])/(Sinh[((γ ϵ ℏ)/2)](t (2 a+γ)-2 a (a+γ) ϵ+2 ϖ) ℏ/(2γ)))]);
S𝔻$g=(Sqrt[((Cosh[(ℏ/2)(Sqrt[(t^2)+(γ^2) (ϵ^2)+4 ϵ ϖ])]-Cosh[((ℏ t-ℏ ϵ γ-2ℏ ϵ a)/2)])/(Sinh[((γ ϵ ℏ)/2)](t (2 a+γ)-2 a (a+γ) ϵ+2 ϖ) ℏ/(2γ)))]);
S𝔻$g=(Sqrt[((2γ(Cosh[(ℏ/2)(Sqrt[(t^2)+(γ^2) (ϵ^2)+4 ϵ ϖ])]-Cosh[((t-ϵ γ-2ϵ a)/(2/ℏ))]))/(Sinh[((γ ϵ ℏ)/2)](t (2 a+γ)-2 a (a+γ) ϵ+2 ϖ) ℏ))]);
S𝔻$g=(Sqrt[((((2γ)/ℏ)(Cosh[(Sqrt[(((t^2)+(γ^2) (ϵ^2)+4 ϵ ϖ)/(4/(ℏ^2)))])]-Cosh[((t-ϵ γ-2ϵ a)/(2/ℏ))]))/(Sinh[((γ ϵ ℏ)/2)](t (2 a+γ)-2 a (a+γ) ϵ+2 ϖ)))]);