Consider a function at time t = 0 such that f(x, 0) = A sin^2 (pi x/a) for 0 les

Question

Consider a function at time t = 0 such that f(x, 0) = A sin^2 (pi x/a) for 0 lessthanorequalto x lessthanorequalto a and f(x, 0) = 0 elsewhere. Choose all of the following statements that are correct about whether this function is a possible wavefunction for a 1-D infinite square well between 0 lessthanorequalto x lessthanorequalto a. It is not a possible wavefunction because it is not in the form A_n sin (n pi x/a). It is not a possible wavefunction because it does not satisfy the time independent Schrodinger equation H psi = E psi. It is a possible wavefunction for two electrons instead of a single electron. A. 1 only B. 2 only C. 3 only D. 1 and 2 only E. none of the above

Explanation / Answer

Answer is A.1 only

Born's first condition for a wave function is not satisfied i.e. the function is not single valued at given value of x and t.

If the function follows first condition , it will be in the form An sin(n*pi*x / a).

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