Originally posted by njoshi3
Hi,
Why is that, the ground state eigenfunction in ANY quantum mechanical system is symmetric under inversion of co-ordinates?
A ground state wave function is a mathematical representation of the lowest energy state of a quantum mechanical system. It describes the probability of finding a particle in a certain location in space at a given time.
The ground state wave function has the lowest possible energy for a system, while excited state wave functions have higher energies. Additionally, the ground state wave function is a stationary state, meaning it does not change with time, while excited state wave functions do change with time.
Yes, the ground state wave function can have both positive and negative values. The square of the wave function, however, which represents the probability of finding a particle in a specific location, is always positive.
The ground state wave function is the solution to the time-independent Schrödinger equation, which describes the behavior of quantum systems. The Schrödinger equation allows us to calculate the ground state wave function for a given system.
The shape of the ground state wave function is directly related to the potential energy of the system. A higher potential energy will result in a narrower and taller wave function, while a lower potential energy will result in a wider and shorter wave function. The actual shape of the wave function is determined by the specific potential energy function of the system.