Schrodinger's equation is a fundamental equation in quantum mechanics that describes the time evolution of a quantum state. It is named after Austrian physicist Erwin Schrodinger and is a central concept in understanding the behavior of particles on a microscopic scale.
A linear equation is one in which the output varies in direct proportion to the input. In the context of Schrodinger's equation, this means that the wave function, which describes the quantum state of a particle, changes in a linear and predictable manner over time.
Schrodinger's equation is used to calculate the probabilities of different quantum states and their evolution over time. It is used in a wide range of fields, including quantum mechanics, chemistry, and materials science, to understand and predict the behavior of particles and systems on a microscopic level.
In most cases, Schrodinger's equation cannot be solved exactly due to its complexity. Instead, scientists use approximations and numerical methods to solve the equation and make predictions about the behavior of quantum systems. However, in certain simple systems, such as the hydrogen atom, an exact solution can be found.
Schrodinger's equation has numerous practical applications, including in the development of new materials and technologies, such as transistors and lasers. It is also used in medical imaging techniques, such as MRI, and in the study of biological systems, such as protein folding. Additionally, it has played a crucial role in the development of quantum computing and cryptography.