(b) Consider a particle confined in a one-dimensional box of length L which has infinite potential energy barriers at x

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B Consider A Particle Confined In A One Dimensional Box Of Length L Which Has Infinite Potential Energy Barriers At X 1 (131.64 KiB) Viewed 46 times

(b) Consider a particle confined in a one-dimensional box of length L which has infinite potential energy barriers at x = 0 and x = L. The potential energy inside the box is zero. (i) State the boundary conditions the wavefunction must satisfy. (ii) Explain why '(x)= Asin(kx) + B cos(kx) cannot be a solution to the [2] = Schrödinger equation for this particle if both A and B are non-zero constants. [2] (iii) = For the wavefunction (x) Asin (kx), sketch the lowest energy wavefunction and the 4th lowest energy wavefunction showing the position (including the value of x) of any nodes. On the same figure sketch ¥(x){ for these two wavefunctions. [3] (iv) Would the value of ſl¥(x)[dx be different or the same for the two 0 wavefunctions in part (iii)? Explain your reasoning. [2]