# Wave Packet in Three Dimensions

Chapter

## Abstract

The position of the classical particle in three-dimensional space is described by the components x, y, z of the position vector:
$$r = \left( {r,y,z} \right)$$
Similarly, the three components of momentum form the momentum vector:
$$p = \left( {{p_x},{p_y},{p_z}} \right)$$
Following our one-dimensional description in Section 3.3, we now introduce operators for all three components of momentum:
$${\hat{p}_x} = \frac{{\hbar \partial }}{{i\partial x}},\quad {\hat{p}_z} = \frac{{\hbar \partial }}{{i\partial y}},\quad {\hat{p}_z} = \frac{{\hbar \partial }}{{i\partial z}}$$
The three operators form the vector operator of momentum,
$$\hat{p} = \left( {{{\hat{p}}_x},{{\hat{p}}_y},{{\hat{p}}_z}} \right) = \frac{\hbar }{i}\left( {\frac{\partial }{{\partial x}},\frac{\partial }{{\partial y}},\frac{\partial }{{\partial z}}} \right) = \frac{\hbar }{i}\nabla$$
Which is the differential operator ▽, called nabla or del, multiplied by $$\hbar /i$$.

## Keywords

Angular Momentum Wave Packet Spectral Function Spherical Harmonic Wigner Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.