Schrodinger Eq. & Energies: Are Values Always Positive?

[oddiseas]

just a question about the energies associted wuth the schrodinger equation> are the energy values always positive values. I thought that since when the eigenfunctions exist the particle is in a bound state, that the energy should be less than that required to escape a bound state and should be negative.

 

[Count Iblis]

just a question about the energies associted wuth the schrodinger equation> are the energy values always positive values. I thought that since when the eigenfunctions exist the particle is in a bound state, that the energy should be less than that required to escape a bound state and should be negative.

Yes, the energies can be negative. However, there must exist a lowest energy eigenvalue, otherwise the system could lose an infinite amount of energy.

 

[Entropia]

Yes, you are correct. In the context of the Schrodinger equation, the energy values are typically negative for bound states and positive for unbound states. This is because the Schrodinger equation is typically used to describe the behavior of particles in a potential well, where the particle is confined to a certain region. In this case, the energy of the particle is lower than the potential energy of the well, resulting in a negative energy value.

However, it is important to note that the energy values in the Schrodinger equation are not always negative for bound states. In some cases, the energy can be positive due to the presence of a repulsive potential or due to the use of a different coordinate system. Additionally, the energy values can also be complex numbers, which can have both positive and negative components.

Overall, the energy values in the Schrodinger equation are not always positive, but they can be positive, negative, or complex depending on the specific system being studied.