The reasoning goes by contradiction : For if the ground state would be degenerate then there would be two orthonormal stationary states | ψ ψ 1 ⟩ and | ψ ψ 2 ⟩ — later on represented by their complex-valued position-space wave functions ψ ψ 1 ( x , t ) = ψ ψ 1 ( x , 0 ) ⋅ ⋅ e − − i E g t / ℏ ℏ and ψ ψ 2 ( x , t ) = ψ ψ 2 ( x , 0 ) ⋅ ⋅ e − − i E g t / ℏ ℏ — and any superposition | ψ ψ 3 ⟩ := c 1 | ψ ψ 1 ⟩ + c 2 | ψ ψ 2 ⟩ with the complex numbers c 1 , c 2 fulfilling the condition | c 1 | 2 + | c 2 | 2 = 1 would also be a be such a state, i.e. would have the same energy-eigenvalue E g and the same spin-state.