Quantum physics is described by a mathematical framework known as quantum mechanics. The fundamental equation that governs the behavior of quantum systems is called the Schrödinger equation. The time-dependent Schrödinger equation for a quantum system is given by:
Ĥψ = iħ∂ψ/∂t
In this equation:
- Ĥ represents the Hamiltonian operator, which corresponds to the total energy of the system.
- ψ is the wave function, which is a mathematical representation of the quantum state of the system.
- i is the imaginary unit (√-1).
- ħ is the reduced Planck's constant, equal to the Planck's constant (h) divided by 2π.
- ∂ψ/∂t represents the partial derivative of the wave function with respect to time.
The Schrödinger equation describes how the wave function of a quantum system evolves over time. It provides information about the probabilities of different outcomes when measurements are made on the system. The solutions to the Schrödinger equation yield the possible wave functions and energy eigenvalues associated with a particular quantum system.
It's worth noting that the Schrödinger equation is just one aspect of the mathematical formalism of quantum mechanics. There are additional equations and principles that govern various aspects of quantum physics, such as the postulates of quantum mechanics, the measurement process, and the mathematical treatment of observables. The full understanding of quantum mechanics requires a deep study of its mathematical foundations and the associated principles and equations.