In quantum mechanics, what is the physical significance of the square of the electronic wave function, |ψ|^2?

• A. It represents the probability density of finding the electron at a particular point in space.
• B. It determines the speed of the electron in its orbit.
• C. It describes the angular momentum of the electron.
• D. It gives the total energy of the electron in an atom.

Answer: (A)

Verified step by step guidance

1. Understand that in quantum mechanics, the wave function \( \psi \) is a mathematical function that contains all the information about the quantum state of a particle, such as an electron.
2. Recognize that the wave function itself can be complex and does not have a direct physical interpretation, but its square magnitude, \( |\psi|^2 \), is very important.
3. Know that \( |\psi|^2 \) represents the probability density function, which means it gives the likelihood of finding the electron at a specific point in space when a measurement is made.
4. Interpret \( |\psi|^2 \) as a spatial distribution: regions where \( |\psi|^2 \) is large correspond to higher probability of locating the electron, while regions where it is small correspond to lower probability.
5. Conclude that \( |\psi|^2 \) does not directly give physical quantities like speed, angular momentum, or total energy, but rather the probability distribution of the electron's position.