Simple question in Del operator on plane wave equation

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Start date Oct 11, 2014
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Del Operator Plane Wave Wave equation

In summary, the Del operator, also known as the gradient operator, is a vector operator used in vector calculus to determine the rate and direction of change of a function at a given point in space. It is used in various equations such as the plane wave equation, Schrödinger equation, Navier-Stokes equation, Maxwell's equations, and the heat equation. It differs from a regular derivative in that it acts on vector functions and can be applied in multiple dimensions. Mathematically, it is represented as the symbol ∇ and is written as ∇ = ∂/∂x i + ∂/∂y j + ∂/∂z k in Cartesian coordinates.

Oct 11, 2014

baby_1

Hello
question is:
As you see when we do del operator on A vector filed in below example it removes exponential form at the end.why does it remove exponential form finally?

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Oct 11, 2014

vela

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It doesn't. The exponential is part of ##\vec{A}##.

1. What is the Del operator?

The Del operator, also known as the gradient operator, is a vector operator used in vector calculus to determine the rate and direction of change of a function at a given point in space.

2. How is the Del operator used in the plane wave equation?

In the plane wave equation, the Del operator is used to represent the spatial derivatives of the wave function. It is commonly used in the Schrödinger equation to describe the behavior of quantum particles in a wave-like manner.

3. What is the difference between the Del operator and a regular derivative?

The Del operator is a vector operator that acts on vector functions, while a regular derivative acts on scalar functions. Additionally, the Del operator can be applied in multiple dimensions, while a regular derivative is typically used in one dimension.

4. How is the Del operator represented mathematically?

The Del operator is represented as the symbol ∇ (pronounced "nabla"). In Cartesian coordinates, it is written as ∇ = ∂/∂x i + ∂/∂y j + ∂/∂z k, where i, j, and k are unit vectors in the x, y, and z directions respectively.

5. What other equations is the Del operator commonly used in?

The Del operator is commonly used in a variety of equations in physics and mathematics, including the Navier-Stokes equation in fluid dynamics, Maxwell's equations in electromagnetism, and the heat equation in thermodynamics.