we derived the wavefunction solutions for an infinite potential well located between 0 x a. By applying the appropriate continuity boundary conditions, the wavefunction simplified to a simple sine function. Using a similar strategy, solve Schrdinger's equation and derive the wavefunction solution for a 1-dimensional infinite potential well centered between-/2 x +/2. (Note: Do not use the slope BC's, they are not truly valid for an infinite potential well model). Derive the normalized wavefunction for the solutions obtained in part (a) above. Plot the normalized wavefunction for the n = 1, 2, and 3 states. Derive the probability function for this system and plot the probability function for the n = 1, 2, and 3 states. Calculate the energy values for the two lowest energy states for an electron in this well where a = 10 (for a well located between -*/2 x +*/2)? Are these values equivalent to the energies derived from the equation we derived in class for an infinite potential well of the same size located between 0 x a? What is the probability that an electron in the ground state (n=1) can be found between 4.9 x 5 . What is the probability that an electron in the n=100 state can be found between 4.9 x 5 ? What is the probability that a classical particle can be found between 4.9 x 5 ?