The energy operator in one-dimension is:

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The energy operator in one-dimension is:

\(i\frac{h}{2\pi}\frac{\partial }{\partial t}\)
\(\frac{i}{h}\frac{\partial }{\partial t}\)
\(-i\frac{h}{2\pi}\frac{\partial }{\partial x}\)
\(-ih^2\frac{d}{dx}\)

Answer 1

CONCEPT:

Schroedinger wave equation:

Schrodinger wave equation is a mathematical expression describing the energy, momentum, and position of the electron in space and time.
The Schrödinger equation (also known as Schrödinger’s wave equation) is a partial differential equation that describes the dynamics of quantum mechanical systems via the wave function.

EXPLANATION:

The one - dimensional time-dependent Schrödinger equation for a free particle is

\(i\frac{h}{2\pi}\frac{\partial \psi \left ( x,t \right )}{\partial t}=\frac{h^{2}}{8\pi^{2}m}\frac{\partial^2 \psi \left ( x,t \right )}{\partial x^2}\)

Where Ψ(x,t) = Wave function, h = Planck constant and m = mass

The energy operator in one-dimension is given by:

\(\hat E = i\frac{h}{2\pi}\frac{\partial }{\partial t}\)

NOTE:

The momentum operator in one-dimension is given by:

\(\hat p =-i\frac{h}{2\pi}\frac{\partial }{\partial x}\)

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The energy operator in one-dimension is:

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