Train Salzburg to Vienna

Train, either ÖBB (Austrian National Railways) or the competitor Westbahn.
Both use the same stations and the same tracks, they compete on price and service levels. Frequent services from both companies, two or more departures per hour for each company, takes 2h25.

See here for all the info you need: https://www.seat61.com/trains-and-routes/vienna-to-salzburg-by-train.htm

Where are you staying in Vienna?

To find the cheapest ticket is tricky, as both OeBB and Westbahn compete with bargain offers, valid under certain circumstances, e.g. on a special weekday, within a given timeframe, bound to a certain train, ticket sold in tobacco shops only, etc.

First of all, you need to define the day of your travel, the time you want to arrive in Vienna, and at what train station there. This would reduce the number of feasible trains drastically. Then you can look for the best offer for that selection.

As far as I know, the cheapest price at the moment is €14 from Salzburg to Vienna.

Thank you all very much. Staying need the medical university

You mean the AKH, I assume. You should take the Westbahn train From Salzburg to Westbahnhof (make sure you get on the correct Westbahn train that ends at Westbahnhof, not Praterstern). From Westbahnhof you take the U6 to the AKH stop.