Question

a.) Explain the physical origins of quantum mechanical tunneling.

b.) In what ways does the quantum mechanical description of a harmonic oscillator merge with its classical description at high quantum numbers?

Answer 1

(a.) Quantum Mechanical Tunelling has its physical origins from long back. The first instance was found due to radioactivity whem Marie and Pierre Curie. They recieved a nobel prize for this. This way people got an idea of half life and radioactive decay.

Then later in 1927 a scientist named Friedrich Hund while studying the well potential and the schrodinger wave equation which deals with different positions a wave can simultaneously exist.It was mathematically applied for an alpha decay. Later this was used for a relationship between half life and the energy of emission. This energy of emission directly depends upon quantum mechanical tunelling.

(b.) The quantum harmonic oscillator is a quantum mechanical model in this area with a known analytical solution. This model matches on a number of points with the analogous description of its classical counterparts. including these points :-

1. The energy levels are quantized, which means only discrete energy values are possible.

2.These energy levels will be equally spaced which is unlike the bohr's theory.

3. This energy is not at zero state but a level above it. This is called zero point energy.Due to this the position and the momentum of the particle is not fixed which again corresponds to the heisenberg uncertainty principle.

4. Moreover coherent states oscillates very much like classical objects.