Creating multiple database at runtime in postgresql

Dear All,

I am new to postgresql database. I want to create an architecture wherein I want to create multiple databases at runtime. To be more description about the purpose, for example
I am creating an account using any application which has postgresql as a backend. I want to create a new database for every user who is creating account then whenever the user login he will be login to his database. I have such kind of setup in MySQL but I would really like to know is it a good idea to have such kind of setup and is it possible in postgresql.

As whenever I create a database in MySQL it gets stored on my hard disk these are file level operations if we use mysql MyIsAM storage engine.

Is it possible to create postgresql database using postgresql stored functions/
Is it possible to have 1000,000 databases on a server?

Please let me know if anyone needs more information on what I am trying to implement.

Any input will be a great help.

Regards,
Manasi