Swiss Rail Pass.

You can book a discount ticket if you can live with a fixed train and date and buy it now. The Austrian Railjet trains go direct from Salzburg to Zurich, the change to a train to Luzern.
Buy at www.sbb.ch/en. During the purchase process they will ask if you have a Swiss Travel Pass (actually it will say "ga", same thing). Then you will only pay the fare from Salzburg to Buchs SG where you enter Switzerland. There, show your pass to the conductor. Once in Switzerland, your free to take any train, so just get on and show your pass and ID when asked.

Choose the schedule you prefer for your travel date using the Deutsche Bahn link at Looking Up Train Schedules and Routes Online. When you view the details for given schedules, it will show the connection points and the border crossing point. Some departures travel through Germany instead of Austria. The Austrian RailJet route (via Innsbruck) is scenic, but also has some construction this summer. The Swiss Travel Pass can start working from the border station, such as Chur, St. Margarethen, Schaffhausen, or perhaps even Basel. It will be prevalidated for that specific date when you buy it online.

schauer, When you are looking up train times and buying tickets you need to spell place names correctly or you will not be successful. It's Salzburg and Luzern.

The trains from Salzburg to Switzerland terminate in Zürich, than you get another train to Luzern, Just look up Salzburg to Luzern, and it will tell you this. If you have a Swiss Pass you just need to buy a ticket to the first station in Switzerland, which is Buchs (SG) on that route. The website will allow you to do that. You don't have to get off the train in Buchs provided you already have your Swiss Pass, you will need to buy it in advance.

Thank you one and all,You have answered my question.