[python] How do I properly set the Datetimeindex for a Pandas datetime object in a dataframe?

I have a pandas dataframe:

    lat         lng         alt days              date        time
0   40.003834   116.321462  211 39745.175405      2008-10-24  04:12:35
1   40.003783   116.321431  201 39745.175463  2008-10-24      04:12:40
2   40.003690   116.321429  203 39745.175521      2008-10-24      04:12:45
3   40.003589   116.321427  194 39745.175579      2008-10-24      04:12:50
4   40.003522   116.321412  190 39745.175637      2008-10-24      04:12:55
5   40.003509   116.321484  188 39745.175694      2008-10-24      04:13:00

For which I am trying to convert the df['date'] and df['time'] columns into a datetime. I can do:

df['Datetime'] = pd.to_datetime(df['date']+df['time'])
df = df.set_index(['Datetime'])
del df['date']
del df['time']

And I get:

                    lat         lng         alt days
Datetime                            
2008-10-2404:12:35  40.003834   116.321462  211 39745.175405    
2008-10-2404:12:40  40.003783   116.321431  201 39745.175463
2008-10-2404:12:45  40.003690   116.321429  203 39745.175521    
2008-10-2404:12:50  40.003589   116.321427  194 39745.175579    
2008-10-2404:12:55  40.003522   116.321412  190 39745.175637

But then if I try:

df.between_time(time(1),time(22,59,59))['lng'].std()

I get an error - 'TypeError: Index must be DatetimeIndex'

So, I've also tried setting the DatetimeIndex:

df['Datetime'] = pd.to_datetime(df['date']+df['time'])
#df = df.set_index(['Datetime'])
df = df.set_index(pd.DatetimeIndex(df['Datetime']))
del df['date']
del df['time']

And this throws an error also - 'DateParseError: unknown string format'

How do I create the datetime column and DatetimeIndex correctly so that df.between_time() works right?

You are not creating datetime index properly,

format = '%Y-%m-%d %H:%M:%S'
df['Datetime'] = pd.to_datetime(df['date'] + ' ' + df['time'], format=format)
df = df.set_index(pd.DatetimeIndex(df['Datetime']))