Müller finished his habilitation at the University of Regensburg with a thesis on the contribution of functional magnetic resonance imaging to the connectivity model of neuro psychiatric diseases in 2003.

[5] Müller completed his doctoral thesis in psychiatric history about the Munich psychiatrist and writer Oskar Panizza with summa cum laude.

In 2012, he created an expert report for the Federal Constitutional Court on the issue of "mental disorder" as part of the Therapy Accommodation Act.

[25][27] Müller researched on the problem of false positives (regarding individuals who were detained preemptively even though they might not have gone on to commit a crime) in danger forecasts: The study by Müller et al. on "Recidivism after Final Rejection of a Subsequent Order of Preventive Detention" is continued after including further cases and excerpts from the Federal Central Criminal Register.

[28][29] Currently, Müller is involved in the construction and the use of virtual reality[21][30][31] in the diagnosis, treatment and risk assessment in forensic psychiatric patients as well as in dangerous offenders in cooperation with the central facility for preventive detention in Lower Saxony Rosdorf.

These aim at establishing professionally anchored lower limits for financial and human resources and call for science-based recommendations on process, structure and outcome of treatments.

Since 2012 Müller has been managing a project funded by the state of Lower Saxony, by the University Medical Center Göttingen and the Asklepios GmbH Niedersachsen on the prevention of sexual abuse (PSM).

[36] Together with P. Briken, Hamburg and M. Rösler, Homburg, Saar, Müller initiated the conference Empirical Research in forensic psychiatry, psychology, psychotherapy (EFPPP) in 2010.