The Schrödinger Equation
The Schrödinger Equation is not an algebraic equation, but a linear partial differential equation. Their are many different types, general, non-relativistic, time-dependent, and time-independent. The time independent equation is associated with the Hamiltonian* operator. The time-independent equation goes like this:
Ĥψ=Eψ
(where Ĥ is the operator, E is the energy of the system, and Ψ is the wave function)
The Schrödinger equation describes the wave function of the system, also known as the quantum state or state vector. A wave function is a probability amplitude** in quantum mechanics*** describing the quantum state of a particle and how it behaves. The equation describes how the quantum state of some physical state can change over time. According to the standard interpretation of quantum mechanics****, the wave function is the most complete description that can be given to a physical system. Solutions to this equations can be used to describe not only molecular, atomic, and subatomic systems, but also to describe macroscopic systems, ranging to possibly the entire universe. Scientists now use this equation to describe the locations of electrons and even other pieces of an atom. Schrödinger discovered this equation in the year 1926. This discovery is often credited as his greatest discovery. It contributed to both quantum physics and the atomic theory.
*Hamiltonian-- The operator corresponding to the total energy of the system.
**Probability amplitude-- A complex number^ whose modulus^^ squared represents a probability or probability density^^^.
***Quantum mechanics--The branch of physics dealing dealing with phenomena that occur at microscopic scales.
****Standard interpretation of quantum mechanics-- Also known as the Copenhagen interpretation, this is one of the earliest interpretations of quantum mechanics. It declares that quantum mechanics does not give a description of an objection reality, but actually deals only with the probabilities of observing and/or measuring different aspects of energy quanta^^^^.
^Complex Number-- A number that can be put into the form a + bi, where a and b are real numbers and i is the imaginary unit, where i squared = −1.
^^Modulus-- Absolute value
^^^Probability Density-- The likelihood for a random continuous variable to take on a given value.
^^^^Energy Quanta-- The fundamental unit of charge, the fundamental unit of energy.
Ĥψ=Eψ
(where Ĥ is the operator, E is the energy of the system, and Ψ is the wave function)
The Schrödinger equation describes the wave function of the system, also known as the quantum state or state vector. A wave function is a probability amplitude** in quantum mechanics*** describing the quantum state of a particle and how it behaves. The equation describes how the quantum state of some physical state can change over time. According to the standard interpretation of quantum mechanics****, the wave function is the most complete description that can be given to a physical system. Solutions to this equations can be used to describe not only molecular, atomic, and subatomic systems, but also to describe macroscopic systems, ranging to possibly the entire universe. Scientists now use this equation to describe the locations of electrons and even other pieces of an atom. Schrödinger discovered this equation in the year 1926. This discovery is often credited as his greatest discovery. It contributed to both quantum physics and the atomic theory.
*Hamiltonian-- The operator corresponding to the total energy of the system.
**Probability amplitude-- A complex number^ whose modulus^^ squared represents a probability or probability density^^^.
***Quantum mechanics--The branch of physics dealing dealing with phenomena that occur at microscopic scales.
****Standard interpretation of quantum mechanics-- Also known as the Copenhagen interpretation, this is one of the earliest interpretations of quantum mechanics. It declares that quantum mechanics does not give a description of an objection reality, but actually deals only with the probabilities of observing and/or measuring different aspects of energy quanta^^^^.
^Complex Number-- A number that can be put into the form a + bi, where a and b are real numbers and i is the imaginary unit, where i squared = −1.
^^Modulus-- Absolute value
^^^Probability Density-- The likelihood for a random continuous variable to take on a given value.
^^^^Energy Quanta-- The fundamental unit of charge, the fundamental unit of energy.