CeCu2Si2 was the first heavy fermion superconductor and unlike those previously discovered, which were well explained by BCS theory, CeCu2Si2 is an unconventional superconductor. Like the high temperature superconductors discovered later, the superconducting mechanism is not understood. The structure of the energy gap of superconductors gives information about the pairing mechanism. Surprisingly, recent measurements show the superconducting gap of CeCu2Si2 is fully open, which is not expected for the d-wave pairing which was believed to occur. Muon spectroscopy measurements may help resolve this mystery. We want to perform measurements in zero field to look for spontaneous magnetic fields in the superconducting state, which will allow us to narrow down the possible pairing states. We will also measure the penetration depth using a transverse field which can probe the gap structure.