As I understand it (and excuse me if I get it wrong or partially wrong), the Schrödinger equation is an energy equation that states that the energy of a quantum system stays constant in time.
So how does it account for vacuum energy?
If it doesn't, how do physicists calculate the evolution of quantum systems while taking into account vacuum energy?
Best Answer
The Schrödinger equation is part of Quantum Mechanics (QM). The vacuum energy is something which pops up in Quantum Field Theory (QFT). QFT is an extension of QM which incorporates special relativity and which makes it natural to create/destroy particles. Technically QFT is a part of QM but it brings so much more to the table that I don't feel bad calling it an extension.
In QM the number of particles is fixed. You can model any number of particles that you want but this number stays the same over time. In QM you could model a vacuum state with zero particles but it would be very boring. It would just be an empty state for all time. In QFT the number of particles can fluctuate and here the vacuum state is very important. The vacuum state is like a blank canvas on which you can paint particles. It also has an energy associated with it and fluctuations as well.
So to answer your question the Schrödinger equation from QM doesn't take into account vacuum energy. To see the vacuum energy you would have to look at the Schrödinger equation equivalent in a QFT.