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

 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

Concept:

• Schrodinger wave equation is a mathematical expression that describes the energy and position of the electron in space and time, taking into account the matter wave nature of the electron inside an atom.

• It is based on three considerations. They are:

  1. Classical plane wave equation, (wave which satisfies 
  2. Broglie’s Hypothesis of matter-wave, (the wavelength of matter-wave is inversely proportional to the linear momentum.)
  3. Conservation of Energy. (total energy = kinetic + potential)

Schrodinger equation gives us a detailed account of the form of the wave functions or probability waves that control the motion of some smaller particles.

The equation also describes how these waves are influenced by external factors.

Moreover, the equation makes use of the energy conservation concept that offers details about the behavior of an electron that is attached to the nucleus.

Explanation:

1. For a wave to be a solution of Schrodinger's equation it must satisfy the following conditions:
   1. The wave function must be a single value.
   2. The wave function must be continuous.
   3. The wave function must be finite.
   4. The wave function must be differentiable at every point in space.
      Hence the correct option is 3.