In general, students of the University and the ETH have the right to attend courses at the other university and earn credit points without additional requirements or fees. Excluded are courses that are offered at one's own university to a comparable level and subject matter. Information can be found at http://www.mnf.uzh.ch/de/studium/reglemente.html.
All UZH students, who complete a performance assessment at the ETH, must be registered (www.rektorat.ethz.ch/de/studium/non-degree-angebote/fachstudierende.html) at the ETH, must book the units of performance and must additionally sign up for the end of semester or end of session exams via myStudies (www.mystudies.ethz.ch). Just like ETH students, UZH students can view their grades on myStudies. In addition, UZH students receive a written confirmation of any performance assessments they took by post.
Attention: auditors at the ETH cannot take exams:https://www.ethz.ch/de/studium/non-degree-angebote/hoerer.html
The Guide to Physics Studies provides comprehensive information about the Bachelor's and Master's programs.