The steady-state form of the Schrodinger wave equation is linear.

Explanation:
The Schrodinger wave equation is a fundamental equation in quantum mechanics that describes the behavior of quantum particles. It is a partial differential equation that relates the wavefunction of a particle to its energy.

The general form of the Schrodinger wave equation is:

Hψ = Eψ

where H is the Hamiltonian operator, ψ is the wavefunction, E is the energy of the particle, and the equation represents the time-independent version of the equation.

The steady-state form of the Schrodinger wave equation refers to a situation where the wavefunction does not change with time. In other words, it represents a stationary state where the probability density of finding the particle does not vary over time.

In the steady-state form, the time-independent Schrodinger equation becomes:

Hψ = Eψ

This equation is linear because it involves the linear operator H acting on the wavefunction ψ. A linear equation is one in which the unknown variable and its derivatives appear only to the first power. In the case of the Schrodinger equation, the unknown variable is the wavefunction ψ, and its derivatives appear only to the first power.

The linearity of the Schrodinger equation has important consequences. It allows for the superposition principle, which states that if ψ1 and ψ2 are two solutions to the Schrodinger equation, then any linear combination of them (e.g., αψ1 + βψ2) is also a solution to the equation. This principle allows for the description of complex quantum systems by combining simpler solutions.

In conclusion, the steady-state form of the Schrodinger wave equation is linear because it involves a linear operator acting on the wavefunction. This linearity allows for the superposition principle and the description of complex quantum systems.