Question

It can easily be verified that the wavefunction of a non-degenerate quantum mechanical system will be real.However the presenter does not explain why this statement is true. How can we prove this? Does the professor assume a real Hamiltonian, i.e. one that includes only kinetic energy and Coulomb interaction terms?

Answer 1

The wavefunction of a non-degenerate quantum system is usually complex, but the observable quantities are obtained from its squared modulus, resulting in real values.

Step-by-step explanation:

In quantum mechanics, the wavefunction of a non-degenerate system is generally complex-valued. However, the physical observables, such as the probability density, are obtained from the squared modulus of the wavefunction, which yields real values. This means that the wavefunction itself may be complex, but when we square it to calculate probabilities, we end up with real numbers.

The assumption of a real Hamiltonian, including only kinetic energy and Coulomb interaction terms, is not necessary to prove this. The wavefunction being real or complex is a general property of quantum mechanics and does not depend on the specific form of the Hamiltonian.