In Quantum mechanics, a wave equation is described bya.first order differential equationb.second order differential equationc.third order differential equation

In quantum mechanics, the wave equation is predominantly described by a second order differential equation. Specifically, the most commonly referenced wave equation is the time-dependent Schrödinger equation, which can be expressed as:

$i\hbar \frac{\partial}{\partial t} \Psi(\mathbf{r}, t) = -\frac{\hbar^2}{2m} \nabla^2 \Psi(\mathbf{r}, t) + V(\mathbf{r})\Psi(\mathbf{r}, t)$

In this equation:

• $i$ is the imaginary unit,
• $\hbar$ is the reduced Planck's constant,
• $\frac{\partial}{\partial t}$ denotes the partial derivative with respect to time,
• $\nabla^2$ is the Laplacian operator, representing the second spatial derivative,
• $V(\mathbf{r})$ is the potential energy, and
• $\Psi(\mathbf{r}, t)$ is the wave function of the quantum system.

The second order nature arises from the fact that the Laplacian involves second derivatives, making it fundamentally a second order differential equation. Therefore, the correct answer is:

Final Answer

b. second order differential equation.