How to add plus 1 day to a timestamp in Cassandra SQL?

Yes, you can specify a time component along with the date arithmetic. In this case, changing 1 to 1d (one day) solves this:

> SELECT studentid,course_date + 1d as nextday FROM students WHERE studentid=1;

 studentid | nextday
-----------+---------------------------------
         1 | 2022-01-04 06:00:00.000000+0000

(1 rows)

For more information, I recently wrote a blog post on the use of Arithmetic Operators in Apache Cassandra 4.0 as well as a short video on this topic! Below is a more comprehensive list of the valid time duration codes:

Valid CQL time duration codes