David Ashworth, 74, from Canterbury, jumped on to the tracks to save 38-year-old Ella Akehurst near Chartham station in Kent last year.
Unable to push Ms Akehurst clear, it is believed Dr Ashworth positioned her so she would not be hurt.
The train passed over Ms Akehurst but killed the father-of-two.
Dr Ashworth was a family friend and "unofficial carer" for Ms Akehurst, who suffered from bipolar disorder, the inquest heard.
He had attended a doctor's appointment with her on the morning of the tragedy after she had woken up feeling tearful, the inquest heard.
Ms Akehurst told officers the pair returned to her parents' home but "the next thing I know I was running down the road" with an urge to "jump from a height".
One witness, Norman Vaughan-Cubitt, saw Ms Akehurst rushing to a footbridge where he said she jumped "without hesitation".
His wife Thelma told the inquest she saw Dr Ashworth arrive in his car as the train got closer, blaring its horn and with its brakes screeching.
Another witness, Michael Kember, described how after the impact, Ms Akehurst said: "How's David? He was trying to help me."
A post-mortem examination found Dr Ashworth died from multiple injuries.
Ms Akehurst, who did not attend the inquest at Margate Magistrates' Court, was in hospital for three months.
Recording a narrative verdict, assistant coroner James Dillon said: "Dr Ashworth had placed himself in a perilous position."
"He may have sacrificed the opportunity of getting himself out of harm's way and, as a result, was hit and killed by the train."
University of Manchester graduate Dr Ashworth - who retired from the University of Kent in 2003 - has been nominated for a posthumous civilian gallantry award from the Cabinet Office.
A retired academic who was killed when he leapt in front of a train to save his friend "may have sacrificed himself", an inquest has heard.