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- Consider a particle of mass m subject to an attractive delta potential V(x) = - Vod(x), where Vo> 0 (Vo has the dimensions of Energyx Distance). (a) In the case of negative energies, show that this particle has only one bound state; find the binding energy and the wave function. (b) Calculate the probability of finding the particle in the interval -a ≤ x ≤ a. (c) What is the probability that the particle remains bound when Vo is (1) halved suddenly. (ii) quadrupled suddenly? (d) Study the scattering case (i.e., E > 0) and calculate the reflection and transmission coefficients as a function of the wave number k.Please asapThe following Eigen function is a typical solution of the time-independent Schrödinger equation and satisfies boundary conditions for a particle in a confined space of a certain length. y(x) = sin (~77) (a) Plot the wave function as a function of x for L = 30 cm and n = 1, 2, 3 and 4. Note: You will need to have 4 plots in the same graph. (b) On a separate graph, plot the probability density (112) as a function of x using the conditions specified in part (a). Note: You will need to have 4 plots in the same graph. (c) Report your observations for parts (a) and (b)