how to set different PYTHONPATH variables for python3 and python2 respectively

I want to add a specific library path only to python2. After adding export PYTHONPATH="/path/to/lib/" to my .bashrc, however, executing python3 gets the error: Your PYTHONPATH points to a site-packages dir for Python 2.x but you are running Python 3.x!

I think it is due to that python2 and python3 share the common PYTHONPATH variable.

So, can I set different PYTHONPATH variables respectively for python2 and python3. If not, how can I add a library path exclusively to a particular version of python?