Quantum Mechanics Homework
Drion Shkreli
Alchemy to Astrophysics
Professor Efthimiades
12/11/2012
Quantum Mechanics Homework
1. Principles of Quantum Mechanics
a. Particles have multiple virtual motions and each motion is accompanied by a wave. The strength of the total particle wave at each point corresponds to the probability that the particle may be found there. Applying this principle we can explain all kinds of phenomena, from the properties of atoms and radioactivity to light reflection.
2. Electron Double Slit Experiment
a. Electrons are fired (possibly one at a time) toward a screen with two slits and each electron that passes through leaves a dot on a film plate. The dots accumulate on specific places, as shown in the diagram below, separated by b lank zones. Therefore, there is a certain probability that an electron may land on C, E, G… and zero probability that it may go to D, F…
b. The probability that an electron may land on some point on the film arises from the interference of two electron virtual waves meeting at that point, one coming from the top slit and the other from the bottom slit. The interference of the infinite electron waves fanning out of the slits produces a succession of high and low intensities of the electron wave function on the film that corresponds to highs and lows of the probability of where the electron may end up.
3. Tunneling
a. This is when a particle can pass through a barrier and come out the other side instead of bouncing back.
b. Consider a particle of kinetic energy E hitting a higher energy V barrier. Most of the incoming particle wave bounces back becoming a reflected wave, but, at the same time, a small part penetrates the barrier and a transmitting wave emerges on the other side. Accordingly, the particle most probably will be reflected, but there is also a small probability that it may transmit over, as if passing through a hidden tunnel, hence the term tunneling.
4.
Alchemy to Astrophysics
Professor Efthimiades
12/11/2012
Quantum Mechanics Homework
1. Principles of Quantum Mechanics
a. Particles have multiple virtual motions and each motion is accompanied by a wave. The strength of the total particle wave at each point corresponds to the probability that the particle may be found there. Applying this principle we can explain all kinds of phenomena, from the properties of atoms and radioactivity to light reflection.
2. Electron Double Slit Experiment
a. Electrons are fired (possibly one at a time) toward a screen with two slits and each electron that passes through leaves a dot on a film plate. The dots accumulate on specific places, as shown in the diagram below, separated by b lank zones. Therefore, there is a certain probability that an electron may land on C, E, G… and zero probability that it may go to D, F…
b. The probability that an electron may land on some point on the film arises from the interference of two electron virtual waves meeting at that point, one coming from the top slit and the other from the bottom slit. The interference of the infinite electron waves fanning out of the slits produces a succession of high and low intensities of the electron wave function on the film that corresponds to highs and lows of the probability of where the electron may end up.
3. Tunneling
a. This is when a particle can pass through a barrier and come out the other side instead of bouncing back.
b. Consider a particle of kinetic energy E hitting a higher energy V barrier. Most of the incoming particle wave bounces back becoming a reflected wave, but, at the same time, a small part penetrates the barrier and a transmitting wave emerges on the other side. Accordingly, the particle most probably will be reflected, but there is also a small probability that it may transmit over, as if passing through a hidden tunnel, hence the term tunneling.
4.