How do I have a date stamp entered when a cell is changed?

I want to autofill the date of an edit in one cell into the next cell. Specifically:

When I enter something into any cell in column 2, I want the cell next to it in column 3 to autofill the date.

I have found a few scripts on here that have pointed me in the right direction, but they will also calculate at other times such as when I delete a tab or make some other significant amendment to the workbook. It also seems to update when I close Google Sheets and then re-open it.

I am currently using script:

function getDate() {  return new Date();}