What is the Schr dinger equation?

The Schrödinger equation is a basic equation in quantum mechanics proposed by the Austrian physicist Schrödinger, and it is also a basic assumption of quantum mechanics, and its correctness can only be tested by experiments. It is a second-order partial differential equation established by combining the concept of matter wave and the wave equation, which can describe the motion of microscopic particles, and each microscopic system has a corresponding Schrödinger equation, and the specific form of the wave function and the corresponding energy can be obtained by solving the equation, so as to understand the properties of the microscopic system.

In quantum mechanics, the state of the system cannot be determined by the value of a physical quantity (e.g., x), but by the function of a mechanical quantity (x, t), that is, the wave function (also known as the probability blessing, state function), so the wave function is called the main object of quantum mechanics research. The question of how the probability distribution of the value of a mechanical quantity and how this distribution changes over time can be answered by solving the Schrödinger equation of the wave function. This equation was proposed by the Austrian physicist Schrödinger in 1926, and it is one of the most basic equations of quantum mechanics, and its position in quantum mechanics is comparable to that of Newton's equations in classical mechanics.

The Schrödinger equation is the most basic equation of quantum mechanics and a basic assumption of quantum mechanics, and its correctness can only be tested by experiments.

Solving particle problems in quantum mechanics often boils down to solving the Schrödinger equation or the stationary Schrödinger equation. The Schrödinger equation is widely used in atomic physics, nuclear physics and solid state physics, and the results of solving a series of problems such as atoms, molecules, nuclei and solids are in good agreement with reality.

The Schrödinger equation applies only to non-relativistic particles that are not too velocity, and it also does not contain a description of particle spins. When relativistic effects are taken into account, the Schrödinger equation is replaced by a relativistic quantum mechanical equation, which naturally includes the spin of the particle.

Schrödinger's fundamental equations for quantum mechanics. Founded in 1926. It is a non-relativistic wave equation.

It reflects the law that describes the state of microscopic particles as a function of time, and its place in quantum mechanics is equivalent to Newton's laws for classical mechanics, which is one of the fundamental assumptions of quantum mechanics. Let the wave function describing the state of the microscopic particle be (r,t), and the Schrödinger equation describing the motion of a microscopic particle with mass m in the potential field v(r,t) is . The wave function (r,t) can be solved given given the initial and boundary conditions and the single-value, finite, continuous conditions satisfied by the wave function.

From this, the probability of the distribution of the particles and the average value (expected value) of any possible experiments can be calculated. When the potential function v does not depend on time t, the particle has a definite energy, and the state of the particle is called the stationary state. The wave function at steady state can be written as the equation (r) is called the stationary wave function, satisfying the stationary Schrödinger equation, which is mathematically called the eigenequation, where e is the eigenvalue, which is the steady-state energy, and (r) is also called the eigenfunction that belongs to the eigenvalue e.

The Schrodinger equation is one of the basic equations describing the motion of particles in quantum mechanics, which was proposed by the Austrian physicist Schrödinger in 1925. It is an equation that describes the evolution of the wave function of a particle over time in quantum mechanics and can be used to calculate the motion state and energy of a particle in various potential fields.

The Schrödinger equation is in the form of:

i\hbar\frac\psi(\mathbf,t)=\hat\psi(\mathbf,t)$$

where $psi(mathbf,t)$ is the wave function of the particle, $hat$ is the Hamiltonian operator, and $hbar$ is Planck's constant divided by $2 pi$.

The physical significance of the Schrödinger equation is that the evolution of the wave signal function of the particle auspicious space over time is determined by the physical process described by the Hamiltonian operator. The Hamiltonian operator contains the kinetic and potential energy of the particle, so it can be used to describe the motion and energy of the particle in various potential fields.

The solution of the Schrödinger equation can be used to calculate the value of the particle's wave function at different locations in time and space. The square of the modulus of the wave function represents the probability density of the particle at that location, so it can be used to ** the probability of the occurrence of the particle at different positions. The solution of the Schrödinger equation can also be used to calculate the energy spectrum of the particle, and thus to obtain the energy distribution of the particle at different energy levels.

The Schrödinger equation is one of the most basic equations in quantum mechanics, and its proposal marks the birth of quantum mechanics. The Schrödinger equation solves a series of phenomena that cannot be explained by classical physics, such as atomic spectroscopy, quantum tunneling, and blind penetration. The successful application of the Schrödinger equation also laid a solid foundation for the development of quantum mechanics.