Tensors for Physics

7.6 Rules for Nabla and Laplace Operators 109

momentum corresponds to the operatorpop=i∇,cf.(7.85). Hence the Hamilton
operator for the kinetic energy of a single particle is

Hkinop=−

^2

2 m

∇μ∇μ=−

^2

2 m

Δ. (7.92)

In accord with the decomposition (7.90) of the Laplace operator into a radial part and
an azimuthal or angular part involving theLoperator, the kinetic energy operator
is the sum a radial part and a part containing the dimensionless angular momentum
operatorL, as defined in (7.86). Thus one has

H

op

kin=−

^2

2 m

Δr+

^2

2 m

r−^2 LμLμ. (7.93)

For the radial partΔrof the Laplace operator see (7.91).