User:Inconspicuum/Physics (A Level)/Quantum Principles

There are two principles which you do not need to know for the exam, but may be helpful in understanding some of the concepts in the course.

Heisenberg Uncertainty Principle
The Heisenberg uncertainty principle states that the momentum and position of an object are limited. Within a certain uncertainty, when we measure a quantum's position, it does not have a definite momentum. When we measure its momentum, it ceases to have a definite position. If we try and measure both, the uncertainty in both will be limited. If we let the uncertainty in our knowledge of momentum be &Delta;p, and the uncertainty in our knowledge of position be &Delta;x:

$$\Delta x \Delta p = \frac{h}{4\pi}$$,

where h is Planck's constant (6.63 x 10-34 Js). The Heisenberg uncertainty principle explains what happens when electrons occupy energy levels - within these levels, they are limited to a certain range of momentums and positions, but it is meaningless to say which exact momentum and position they occupy. If we measure the momentum with no uncertainty, then the uncertainty in position becomes infinite, and vice versa.

Pauli Exclusion Principle
The Pauli exclusion principle states that no two fermions (a set of particles including the electron) may occupy the same quantum state as each other. In layman's inaccurate terms, this means that, although two such particles can be in the same place as each other, if they are, they will be moving at different velocities and so will shortly no longer be in the same place as each other.

This is why, for example, electrons appear to have 'shells' - there is only a limited number of quantum states that the electrons can occupy, so some have to occupy a different 'shell'. Also, without the Pauli exclusion principle, matter would collapse in on itself - the attractive forces between particles are greater than the repulsive forces. However, the moment they try and do this, then they must be moving at different velocities, and so no longer be collapsing in on each other.