The Schengen Agreement
Sweden is part of the Schengen Agreement, an agreement on unrestricted travel for persons in Europe. This co-operation only regulates the control of persons as travellers, and does not affect EU regulations for the free transport of goods, services and capital.
Travel in the Schengen area is equivalent to domestic travel in terms of the control of persons. You therefore do not need to show your passport when travelling between the Schengen countries, but you still need to bring your passport since you need to be able to confirm your nationality in various circumstances when visiting another Schengen country.
Travellers to or from the Schengen area will go through a personal control, both on arrival and departure. Identity will be checked, as well as the validity of the passport. Travellers will also be checked in relation to a joint police register (Schengen Information System).
If you are travelling to another Schengen country everything will be more or less the same. You can find more information about Schengen at Swedavia website.
Find out more about Passports and Visas to Sweden