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DuckAmuck
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Is the following true?
ψ*∇^2 ψ = ∇ψ*⋅∇ψ
It seems like it should be since you can change the direction of operators.
ψ*∇^2 ψ = ∇ψ*⋅∇ψ
It seems like it should be since you can change the direction of operators.
No. It is definitely not generally true.DuckAmuck said:Is the following true?
ψ*∇^2 ψ = ∇ψ*⋅∇ψ
It seems like it should be since you can change the direction of operators.
You can do that for hermitian operators. But the derivative is not a hermitian operator. It is an anti-hermitian operator, due to the minus sign explained in the previous post.DuckAmuck said:It seems like it should be since you can change the direction of operators.
The nabla operator, denoted as ∇, is a mathematical operator used in vector calculus to represent the gradient, divergence, and curl of a vector field. In the context of wave functions, the nabla operator is used to describe the spatial variation of the wave function.
The nabla operator is applied to a wave function by taking the partial derivatives of the wave function with respect to each spatial coordinate. This results in a vector quantity known as the gradient of the wave function.
In quantum mechanics, the nabla operator is used to describe the spatial behavior of particles and their associated wave functions. It is a fundamental tool in understanding the behavior of quantum systems and is used in many important equations, such as the Schrödinger equation.
The nabla operator affects the shape of a wave function by describing the rate of change of the wave function in different directions. This can result in changes to the amplitude and phase of the wave function, ultimately affecting its overall shape.
Yes, the nabla operator can be applied to all types of wave functions, including scalar, vector, and tensor wave functions. However, the specific form of the operator and its effects on the wave function may differ depending on the type of wave function being considered.