Laws of Science - Laws of Quantum Mechanics

Laws of Quantum Mechanics

Quantum mechanics has its roots in postulates, these lead to results which are not usually called "laws", but have the same status. One postulate that a particle (or a system of many particles) is described by a wavefunction, and this satisfies a (quantum) wave equation (the Schrödinger equation or some other relativistic wave equation). Solving this wave equation predicts the time-evolution of the system's behaviour, analogous to solving Newton's laws in classical mechanics.

Other postulates change the concept physical measurement (using quantum operators), that some measurements can't be done at the same instant of time (Uncertainty principles), and particles are fundamentally indistinguishable.

Quantum field theory Schrödinger equation (general form): Describes the time dependence of a quantum mechanical system. The Hamiltonian (in quantum mechanics) H is a self-adjoint operator acting on the state space, (see Dirac notation) is the instantaneous quantum state vector at time t, position r, i is the unit imaginary number, ħ = h/2π is the reduced Planck's constant.	Wave-particle duality Planck–Einstein law: the energy of photons is proportional to the frequency of the light (the constant is Planck's constant, h). De Broglie wavelength: this laid the foundations of wave-particle duality, and was the key concept in the Schrödinger equation, Heisenberg uncertainty principle: Uncertainty in position multiplied by uncertainty in momentum is at least half of the reduced Planck constant, The uncertainty principle can be generalized to any pair of observables - see main article.
Wave mechanics Schrödinger equation (original form):
Pauli exclusion principle: No two identical fermions can occupy the same quantum state (bosons can). Mathematically, if two particles are interchanged, fermionic wavefunctions are anti-symmetric, while bosonic wavefunctions are symmetric: where ri is the position of particle i, and s is the spin of the particle. There is no way to keep track of particles physically, labels are only used mathematically to prevent confusion.