Prob. 3: Manifestation of quantum phenomena (total 25 points) (a)-(e) 5 points each. Please provide some experimental demonstration or explanation of natural observations or characteristics of application which confirm(s) / display(s) the following notion of quantum physics. In either experiments or observation, please attach a brief explanation and justification to your statement.
3-(A) Vibration of molecules can be treated by quantum mechanics using a parabolic potential. In classical cases, we can use mass(es) attached to a spring. In quantum mechanics, energy levels are quantized, unlike classical oscillators. How can you demonstrate that?
3-(B) The ground state energy of classical oscillator is zero, while that of quantum oscillators has finite (zero-point) energy. How can you demonstrate that (not by calculations but by some experiments or observations)?
3-(C) Electrons can have both orbital and spin angular momentum, and associated magnetic moment. There are two spin quantum numbers (+1/2 or -1/2) for an electron. Describe some quantum phenomena or observation which demonstrate(s) that an electron has a spin 1/2.
3-(D) Laser light is a coherent light. Which property of laser depends on this feature? What application is related to the coherence?
3-(E) Quantum particle(s) can tunnel through a potential barrier.

3A. This phenomenon can be seen in the discrete emission of the molecules.

3B. The emotion of the atoms is observed, from states high in energy to a state of minimum energy that is stable indefinitely.

3C. When an electron beam passes through an inhomogeneous magnetic field, it is divided into only two beams

3D. This is due to the stimulated emission

3E. The penetration of a potential barrier is observed in the radioactive emission of heavy atoms, where an alpha particle (Helium nucleus)

Explanation:

This problem asks for some experimental explanations of various quantum phenomena.

3A. This phenomenon can be seen in the discrete emission of the molecules.

In the classical explanation all states or energies are allowed, therefore when emitting energy (photons) there should be a continuum, this is not observed

In the correct quantum explanation only some states are allowed, therefore the emission must be discrete, which is observed in the emission or absorption of molecules and atoms

3B. The emotion of the atoms is observed, from states high in energy to a state of minimum energy that is stable indefinitely.

The incorrect classical explanation that if the minimum energy was zero the electrons cannot rotate around the nuclei and the atom collapses, this does not happen

3C. When an electron beam passes through an inhomogeneous magnetic field, it is divided into only two beams, which is evidence of the existence of two discrete states that we call spin, remember that a free electron beam has zero angular momentum.

3D. This is due to the stimulated emission that occurs when a photon passes through the emission zone, causing the atoms to have transitions and these emitted photons have the same initial photon location, the laser beam all photons are in phase and therefore it is coherent .

This is widely used for holographic and interference work

3E. The penetration of a potential barrier is observed in the radioactive emission of heavy atoms, where an alpha particle (Helium nucleus) leaves the atomic nucleus penetrating the barrier since its energy is lower than the nuclear barrier potential.