Quantum mechanics has the following basics; wave duality, discrete energy, position and momentum, quantum states, quantum numbers, wave amplitude, and wave function.
Wave duality is the property of a particle to behave both as a wave and a particle. Photons are quantum particles related to electromagnetic waves (â€œQuantum Mechanicsâ€, par 7). These photons have a definite amount of energy. The energy depends on the frequency of the associated wave. The energy is given by E = hf.
The second one is discrete energy. The measure of energy in particles is not continuous. They do not take any value but take certain definite values. Here, energy is discrete in nature. Angular momentum of various systems only comes in whole numbers. These are multiples of h/2. They do not come in decimals or fractions.
Real numbers do not represent position and momentum in quantum mechanics as it is in classical mechanics. They are Hermitian linear operators acting in ket space. This will represent all possible situations of a system (Fitzpatrick, Pp 33).
Quantum states and numbers are parameters used to describe systems in quantum mechanics. States describe the position of a particle, for example, the orbital. Quantum numbers define quantities related to the state. Such quantities are electric charge, angular momentum, and energy. They can only have certain distinct values confined in the quantum system.
Wave amplitude and function are for describing states. Probability amplitude is an intricate number function of position. Its quantity is definite at any point in space.