Demonstrate that there is approximately 16% probability (P) of finding the ground state harmonic oscillator displaced beyond the classical turning points. What phenomenon does this demonstrate?

The probability of finding a particle in a space is proportional to the square of its absolute value.

In quantum mechanics, there are still chances of find a particle in a classically forbidden region.

That is, finding the ground state harmonic oscillator displaced beyond the classical turning points.

Since there is a chance for finding the ground state harmonic oscillator displaced beyond the classical turning points, the probability (P) will have a value and not equal to Zero( I.e 16%).

By normalization, the probability can be added to 1

This phenomenon is tunneling in quantum mechanics.

Step-by-step explanation:

The motion of a classical oscillator is confined to the region where its kinetic energy is nonnegative.

Physically, it means that a classical oscillator can never be found beyond its turning points, and its energy depends only on how far the turning points are from its equilibrium position. The energy of a classical oscillator changes in a continuous way. The lowest energy that a classical oscillator may have is zero, which corresponds to a situation where an object is at rest at its equilibrium position. The zero-energy state of a classical oscillator simply means no oscillations and no motion at all (a classical particle sitting at the bottom of the potential well.

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.