I would use unistrut. Mount one piece to the wall through at least two studs with the U facing up. You can drill a larger hole through the far side to allow the screw to pass through as you fasten it with size 10-12 screws (not drywall screws). Bolt a second piece to the inside of the door below the window sill with the U facing down. Then just hang the door on the strut. You can screw a wood block to the bottom inside of the door so it hangs parallel to the wall of let it angle in naturally so it gives a better viewing angle.
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Bill