Application Of Schrodinger Wave Equation – MSQ - Physics MCQ

The correct answers are:  for infinite case &  for finite case  for infinite case &   for the finite case 

The Steady-state Schrodinger Wave equation is a linear in the wave function Ψ. It means, that no term has \Psi with a degree greater than 1.

 is normalised, so is  & neither of has any time dependence.

The correct answers are: If  is normalised, then  has to be normalised, Neither of &  has any time dependence

The solution of a symmetric infinite potential well consists of 

Now, any function can be written as a linear combination of these functions (sin and cos)

∴ They form a complete let

The correct answers are: They are alternately even and odd with respect to the centre of the well, As we go up in energy, each successive state has one more node. i.e.  ψ₁(x) has none, ψ₂(x) has one, ψ₃(x) has 2 and so on, They are mutually orthogonal, They form a complete set

The correct answers are: 

Energy levels are same!

The correct answer is: Energy levels are same,  in both cases.

Probability is 0 at x = 0 & a
For 

Probability density is zero at x = 0, a/2 , a

Probability density zero at x = 0, 

The correct answers are: 

The Schrodinger equation solution are 

∴  momentum eigenfunction.

The correct answers are: The Schrodinger equation yields the solution to be  (linear combination of the two), The solutions of the Schrodinger equation are both energy and momentum eigenfunctions

The correct answers are: The gradient of the solution must be single valued, finite and continuous at the every point, The gradient should also be bounded at large distances, The wave function must be continuous throughout, The wave function must vanish at the point where the potential approaches infinity

 for a harmonic oscillator

 

∴   evenly spaced.

The correct answers are: A spectrum of evenly spaced energy levels, A non zero probability of finding the oscillator outside the classical turning points