1. Two delta functions [15 points] Consider a particle of mass m moving in a one-dimensional double well potential V(x)

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1 Two Delta Functions 15 Points Consider A Particle Of Mass M Moving In A One Dimensional Double Well Potential V X 1 (76.5 KiB) Viewed 122 times

1. Two delta functions [15 points] Consider a particle of mass m moving in a one-dimensional double well potential V(x) = −g8(x − a) — g8(x + a), g> 0. (a) Find transcendental equations for the bound state energy eigenvalues of the system. Plot the energy levels in units of ħ²/(ma²) as a function of the dimen- sionless parameter λ = mag/h². Explain the features of the plot. (b) In the limit of large separation 2a between the wells find a simple formula for the splitting between the ground state and the first excited state.