Passive form

This sentence should read as:
The door was knocked on by a postman.

It is also passive.

If you changed this to:

Babies should be looked pleasantly after by their parents.

You could have a split infinitive too.

They must be passive sentences because they make my skin itch. That's how I usually tell.

Many grammarians think the rule against splitting infinitives is nonsense. The only reason it is frowned upon is that you can't do it in Latin (which is a pretty stupid reason). You should feel free to proudly split infinitives when the opportunity arises.

I would never use the word "pleasantly" that way. It think this is a word choice problem rather than a grammar problem.

"Babies should be carefully looked after by their parents." This sounds a lot better to my ears.

This link says 'knock' is an Intransitive Verb. http://www.grammar-quizzes.com/passive1d.html
I cannot understand.

Hi Jane

Knock has lots of meanings and submeanings. You can certainly 'knock a door' - but it isn't the same as 'knock on a door' in normal usage.
'Knocking on a door' is the act of hitting it to make a noise to attract the attention of someone on the other side of it.
'Knocking a door' could mean bumping into it accidentally while carrying something through it or past it - or (more idiomatically) making disparaging remarks about the door.

Someone would understand what you meant but it would sound a little funny to most native English speakers.

Sorry English is such a stupid language. (That's me knocking English)

The likelihood of it ever being a real English sentence in use is small indeed.