Hi. Welcome to Just Answer.
What you need to do is stop the drum effect. This is where the drywall attached to the studs acts like a drum to transfer the sound to your apartment from theirs.
If you can break that connection the sound will be reduced 80%.
Dan please see the last post. I was editing it when you viewed it (i think??)
I guess I should have been more specific. There is a layer of cinderblock between my neighbor's drywall and mine, and no studs or anything to separate the cinderblock from the drywall. Because I live in an apartment, I can't remove drywall or anything permanent like that. Also, what about soundproofing the window without making any permanent modifications? I don't need perfect 100% soundproof, just something that will block *most* sound.
This should work for you.
As for the window applying some window tint helps to eliminate a lot of the sound transmitted by the glass.
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