「神様のカルテ」テーマ曲　辻井伸行

His own composition - "神様のカルテ" by Nobuyuki Tsujii - or as Google translate would have it 'God's medical record'

Wikipedia

Kamisama no Karute (神様のカルテ?) is a 2011 Japanese film directed by Yoshihiro Fukagawa. The film is based on the bestselling novel of the same name by an actual doctor.

Dr. Ichito Kuriharai (Sho Sakurai) works at a clinic in Nagano Prefecture. He rarely has any free time due to the clinic's shortage of doctors and the constant influx of patients. Ichito even sometimes diagnoses patients out of his area of specialty and sometimes goes days without sleeping. He hopes to work at a major hospital where he can get more free time to spend with his wife Haruna (Aoi Miyazaki) and also specialize in his field of study. However, Ichito is also reluctant to add to shortage of doctors at the clinic and break his relationships with the patients.

One day, Dr. Ichito Kuriharai clears out the belongings of a terminal cancer patient who died. During this time, he discovers a letter made out to him thanking him for the care he provided to her, even though he could not cure her sickness. Dr. Ichito Kuriharai then has a revelation about the medical chart he keeps in his hand - filled with personal observations and concerns...