Next time, get a falcon.

I'd hire an assassin or Nuke them

Put out a pile of raw uncooked white rice for a week or two and they won't be there anymore. When the birds eat the rice raw they fill themselves up and as their stomach start to digest the rice it expands and kills the bird. Which is the reason nobody throws rice at a bride and groom anymore after they get married.

Birds just need to die

You can use sticky chemicals on railings or anywhere they may want to roost. They hate anything sticky on their "feet". Anti roosting spikes are sold at hardware stores. Pigeons breed extremely fast; six times a year. It is safe to cut up birth control and feed it to them to reduce their populous and is even recommended by the leading animal welfare groups; birth control represents a "bird friendly" solution for pigeon control. Good luck!

I'd rather have pigeons near my window than you, OP.. Just sayin'.

Why not post a plastic owl or hawk, and sounds of those animals feeding young. Works great in keeping them away at the job! Figured that is better than breaking window panes!

If you tie a carrier bag out there that keeps them away. They don't like it flapping about in the wind. Of course having a carrier bag tied to your veranda isn't the most attractive..

Take a piece of construction paper and tape it to stick off of your railing. Then glue a piece of popcorn to the end of it.

... A short, sharp knock? With your hand, a knock as you describe wouldn't break the glass. Did you use a tool or did you really slam your hand into the window? Either way YDI!