A Gaussian wavefunction is a mathematical function used to describe the probability distribution of a quantum particle in space. It is often used to represent the electron density in an atom or molecule.
The expectation energy is the average energy that a particle would have if it were in a particular state described by the wavefunction. In the case of a Gaussian wavefunction, the expectation energy is directly related to the position of the particle and can be calculated using the Schrӧdinger equation.
No, a Gaussian wavefunction is specifically used to describe quantum particles, such as electrons, in a probabilistic manner. It cannot be used to describe classical particles, such as those in Newtonian physics.
The normalization of a Gaussian wavefunction ensures that the total probability of finding a particle in all possible positions is equal to 1. This is a necessary condition for probability distributions and ensures that the wavefunction accurately describes the behavior of the particle.
Yes, there are some limitations to using a Gaussian wavefunction. It assumes that the potential energy is constant, which is not always the case in real systems. Additionally, it cannot accurately describe systems with multiple particles or interactions between particles.