title: Pandas adding Time column to Date index
body: <p>I have a dataframe, Date index type is <em>Timestamp</em>, Time column is <em>datetime.Time</em>:</p>
  
  <pre><code>            Time  Value
  Date
  2004-05-01  0:15  3.58507  
  2004-05-02  0:30  3.84625
                ...
  </code></pre>
  
  <p>How do I convert it to:</p>
  
  <pre><code>                    Value
  Date
  2004-05-01 0:15     3.74618
  2004-05-01 0:30     3.58507
  2004-05-01 0:45     3.30998
  </code></pre>
  
  <p>I wrote a code which does work, but it's not very pythonic:</p>
  
  <pre><code>ind = frame.index.get_level_values(0).tolist()
  tms = frame['Time']
  new_ind = []
  for i in range(0, len(ind)):
      tm = tms[i]
      val = ind[i] + timedelta(hours=tm.hour, minutes=tm.minute, seconds=tm.second)
      new_ind.append(val)
  
  frame.index = new_ind
  del frame['Time']
  </code></pre>