In the south of Sweden you can travel by train with Öresundståg, a joint train service system. You can for example purchase your train ticket to Göteborg (Gothenburg) at Skånetrafiken.
You can travel with Öresundstag to 52 destinations, for example Göteborg 
(Gothenburg) and Växjö-Alvesta
Please observe when traveling between Malmö-Göteborg (Gothenburg) and Malmö –Alvesta/Växjö.
The rail system between Malmö –Göteborg and Malmö-Alvesta/Växjö is also used by SJ. Make sure that you board a "Öresundståg" train.
More information about Öresundståg
Read more about travel between counties in south of Sweden at
www.oresundstag.se