5 Days 4 Night Trip - Please advice

I am planning for a 5 days 4 nights trip to Switzerland with my wife from Germany.
we would like to visit Lucerne (Mt Pilatus),Zermatt,Interlaken,Montreux,Bern. Please suggest the best route.
Thinking of staying in Lucerne all 4 nights.

Day 1 - 21st April: Reach Lucerne at 1 PM.
...
Day 5 - 25th April: Train from Lucerne to Germany. (10 PM)

Places:
Lucerne - Mt.Titlis or Mt.Pilatus, Lake, Museum.
Zermatt - Glacier Express, Gornergrat, Matterhorn Museum
Lake Breinz or Lake Thun - Boat trip.
Interlaken places, Jungfrauloch or Schilton
Montreaux - Golden Pass train, Chillon Castle
Bern City Tour

Stay:
Is it fine to stay in Lucerne or any other recommended place?

Pass:
Should we take Swiss pass or any other pass for this plan? Please advice.

Thanks in advance.

Hello nehemoo,

Your wish list is quite long for a 5 day stay. You would have to travel a lot on most days, but it can be done. If you prefer one base town, you could look into Bern, Thun, Spiez or Interlaken. Lucerne is too far away for a day trip to Zermatt. You'd best skip the Glacier Express. It's a one day trip from Zermatt to St. Moritz, and it does not fit into your itinerary. I recommend to find the travel details for all trips in the timetable and then see whether the travel times are acceptable to you.

You do indeed need a Swiss Pass. A 4-day pass would be sufficient if you stay in town the first day, or buy a point to point ticket for the last day. See here for prices and more pass details.