Write schrodinger wave equation and explain the terms involved in it?

Question: Write schrodinger wave equation and explain the terms involved in it?

The Schrödinger wave equation is a mathematical expression that describes the dynamics of quantum mechanical systems via the wave function. The wave function is a probability wave that encodes the information of the position and energy of a subatomic particle. The equation takes into account the matter wave nature of the particle. There are two versions of the equation: the time-dependent and the time-independent Schrödinger equations. The former describes how the wave function changes over time, while the latter relates the wave function to the energy of the system.

The Schrödinger equation can be written as:

$$i\hbar \frac{\partial}{\partial t}\Psi(r,t) = \hat{H}\Psi(r,t)$$

where $\hbar$ is Planck's constant divided by $2\pi$, $\Psi(r,t)$ is the wave function, $\hat{H}$ is the Hamiltonian operator.

The terms involved in this equation are:

- $i$ is the imaginary unit.

- $\hbar$ is Planck's constant divided by $2\pi$.

- $\frac{\partial}{\partial t}$ is a partial derivative with respect to time.

- $\Psi(r,t)$ is the wave function.

- $\hat{H}$ is the Hamiltonian operator.

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