It's not possible, browsers cannot open Photoshop documents. Same with .doc but as far as I know IE could do that by embedding MS Word in the browser window if it's installed - however, I'm not sure if this works on current IE versions, even if it does I wouldn't rely on this feature to be available to most people.
You could try using PHP to convert .psd to .jpg or .png with ImageMagick and displaying it in the browser. However, this will work only for .psd files saved with compatibility option.
In other words - internet browser is not Photoshop and cannot open Photoshop files. You would need to install a Photoshop plugin in your browser, however, I don't know if it even exists.