Chapter 40, Problem 40.1DQ

To determine

To explain: Why the wave function is not used for describing the macroscopic bodies.

Answer to Problem 40.1DQ

The macroscopic bodies does not possesses wave nature in a physically significant order or they cannot be considered as in a state of wave particle duality and assigning a wave function for a macroscopic body worth no use in describing their state and dynamics. So the wave function is not used for describing the macroscopic bodies such as baseballs and cars.

Explanation of Solution

According to the wave particle duality, every material body is associated with a wave with wavelength given by de Broglie as,

$\lambda =\frac{h}{mv}$

Here,

$\lambda$ is the de Broglie wavelength

$h$ is the Planck’s constant

$m$ is the mass of the particle

$v$ is the velocity of the particle

The wavelength associated with macroscopic bodies is very small and insignificant (in the order of ${10}^{-40}$ m) due to their large mass and small velocity and hence their wave nature is not observable. The wave nature is observed in the microscopic scale only (for elementary particles). The wave function is the mathematical function, which varies when a wave or particle with significant de Broglie wavelength traverses through space. Since the wave nature of macroscopic bodies are not physically observed, assigning a wave function for such bodies worth no use in describing their motion and behavior. Moreover the macroscopic bodies exhibit no superposition but the microscopic bodies exhibit superposition of the waves associated with them and hence they exist in the superposed state whose properties and dynamics can be explained using the wave function.

Conclusion:

Thus, the macroscopic bodies does not possesses wave nature in a physically significant order or they cannot be considered as in a state of wave particle duality and assigning a wave function for a macroscopic body worth no use in describing their state and dynamics. So the wave function is not used for describing the macroscopic bodies such as baseballs and cars.