QED symbol in latex

You can use \blacksquare ■:

When creating TeX, Knuth provided the symbol ■ (solid black square), also called by mathematicians tombstone or Halmos symbol (after Paul Halmos, who pioneered its use as an equivalent of Q.E.D.). The tombstone is sometimes open: □ (hollow black square).

If you \usepackage{amsmath}, the \blacksquare command will typeset a solid black square. The \square command will give you a hollow square.

The ulsy package has a few version of the lightning bolt for contradictions: \blitza, \blitzb, ..., \blitze. Just drop \usepackage{ulsy} into the preamble of your document.

Finally, as others have pointed out, the Comprehensive LaTeX Symbols List is a great resource for finding the perfect symbol for the job.

What about \blacksquare? http://amath.colorado.edu/documentation/LaTeX/Symbols.pdf

The question specifically mentions a full box and not an empty box and not using proof environment from amsthm package. Hence, an option may be to use the command \QED from the package stix. It reproduces the character U+220E (end of proof, ∎).