1) Adeep 2) Deep 3) Deeply 4) Intensely 1) Deeply 
• (adv.) In a profound manner.
Pro·found'ly adverb In a profound manner. « Why sigh you so profoundly ?» Shak. 
[adv] - to a great depth psychologically
profoundly 1. A reference to having intellectual depth and insight. 2. Descriptive of something which is difficult to fathom or to understand. 3. Extending far below the surface. 4. Coming from, reaching to, or situated at a depth.
deeply adverb to a great depth psychologically; `They felt the loss deeply`