Quantum States And Operators - SS3 Physics Lesson Note

In quantum mechanics, a quantum state is a mathematical description of a physical system. Quantum states are represented by wavefunctions, which are complex-valued functions that describe the probability amplitude of a quantum system being in a particular state. The wavefunction contains all the information about the system that can be obtained from measurements.

Quantum operators are mathematical entities that operate on quantum states to produce new states. These operators represent physical observables such as position, momentum, and energy, and they are represented by Hermitian matrices. When an operator is applied to a wavefunction, the result is another wavefunction that represents the system in a new state.

The behavior of quantum systems is determined by the Schrödinger equation, which relates the time evolution of a quantum state to the Hamiltonian operator, which describes the energy of the system. The solution of the Schrödinger equation gives the wavefunction of the system at any given time, and it allows for the prediction of the probabilities of different outcomes of measurements.

In summary, quantum states and operators are fundamental concepts in quantum mechanics that describe the behavior and properties of physical systems at the microscopic level. They are used to calculate probabilities of different outcomes and make predictions about the behavior of quantum systems.