Make some additions to the Hamiltonian operator.
What follows is a vector, but looking at this vector alone is meaningless.
It only makes sense when this function needs to be put together with other functions to perform operations.
Gradient divergence and curl
gradient
The blue part is the gradient of a scalar.
We multiply this scalar with the operator (the following is the vector multiplied by the scalar)
We multiply f in and get the derivative of f with respect to x, y, z
Divergence
The function that divergence deals with is a vector function
We use this operator and F (vector function) to perform dot multiplication (multiply the corresponding positions and then add)
Curl
The function processed is also a vector function (but here it is a cross product ), the divergence is a dot product, and the curl is a cross
product. The determinant is a vector (I always thought it was a number...)
Laplacian operator (equilateral triangle)
It is the divergence of the gradient; it is dealing with a scalar function.
First calculate the gradient for f, and then calculate its divergence for the gradient. It
becomes the second derivative of f with respect to x (the same for y and z).
I is the dividing line. --------------------
First distinguish between quantity fields and vector fields
After the quantity field
nabla acts on the function, we get such a vector, turning the quantity field into a vector field
The nabla operator turns the vector field into a quantity field through inner product
The divergence is 2, which is a local description of a flux (the divergence is the volume density of the flux)
and is cross-multiplied (turning the vector field into a vector field).
Curl: is a local description of the ring quantity.