df = pd.DataFrame({"Price":[120, 240, 350, 460, 500], "Date":["2020-02-01", "2020-08-12", "2021-04-10", "2021-10-20", "2022-03-19"]})
datetime_series = pd.to_datetime(df["Date"])
datetime_index = pd.DatetimeIndex(datetime_series.values)
new_df=df.set_index(datetime_index)
new_df.drop('Date',axis=1,inplace=True)
print(new_df)
#output
# Price
#2020-02-01 120
#2020-08-12 240
#2021-04-10 350
#2021-10-20 460
#2022-03-19 500