1. A quantum particle of mass m is subject to the anti-symmetric double delta potential given by V(x) = Vo [d(x + a) — 8(x − a)] - - where Vo is a positive real constant and a > 0. Solve the bound state energy/ies of the particle in this potential by following the instructions outlined below. (a) Write down and solve the time-independent Schrodinger equation for each region: (I) x < -a, (II) −a < x < a, and (III) x >a. (b) By applying the boundary conditions at x = −a and at x = a, derive the four equations relating the wave functions between two adjacent regions, and its first derivatives between the adjacent regions. (c) Derive and solve the transcendental equation for the bound state energies. You may use graphical methods. Write down the expression for the bound state energy/ies.

1. A quantum particle of mass m is subject to the anti-symmetric double delta potential given by V(x) = Vo [d(x + a) — 8(x − a)] - - where Vo is a positive real constant and a > 0. Solve the bound state energy/ies of the particle in this potential by following the instructions outlined below. (a) Write down and solve the time-independent Schrodinger equation for each region: (I) x < -a, (II) −a < x < a, and (III) x >a. (b) By applying the boundary conditions at x = −a and at x = a, derive the four equations relating the wave functions between two adjacent regions, and its first derivatives between the adjacent regions. (c) Derive and solve the transcendental equation for the bound state energies. You may use graphical methods. Write down the expression for the bound state energy/ies.