df = pd.DataFrame({'my_timestamp': pd.date_range('2016-1-1 15:00', periods=5)})
>>> df
my_timestamp
0 2016-01-01 15:00:00
1 2016-01-02 15:00:00
2 2016-01-03 15:00:00
3 2016-01-04 15:00:00
4 2016-01-05 15:00:00
df['new_date'] = [d.date() for d in df['my_timestamp']]
df['new_time'] = [d.time() for d in df['my_timestamp']]
>>> df
my_timestamp new_date new_time
0 2016-01-01 15:00:00 2016-01-01 15:00:00
1 2016-01-02 15:00:00 2016-01-02 15:00:00
2 2016-01-03 15:00:00 2016-01-03 15:00:00
3 2016-01-04 15:00:00 2016-01-04 15:00:00
4 2016-01-05 15:00:00 2016-01-05 15:00:00