The Hakurouken (白楼剣) and Roukanken (楼観剣), are weapons used by Youmu Konpaku. Roukanken, or the Lookout-Tower Sword, is a long-bladed katana said to be made by youkai and cannot be wielded by normal humans. It's said that it has the power to kill ten spirits in one stroke, but as one cannot actually kill spirits, the truth of this claim is debatable. Youmu herself claims that that "The things that cannot be cut by my Roukanken, forged by youkai, are close to none!". Perfect Memento echoes this claim (it's likely that Akyu is simply quoting Youmu on this, though.). The Hakurouken, or the White Tower Sword, is the ancestral sword of the Konpaku family. It has the power to dispel the confusion of those it cuts. That is, using it on ghosts will cause them to attain enlightenment (Shikieiki has said that what Youmu's doing to the spirits is a form of "cheating"), and using it on humans will cause them discomfort and a bit of pain.
Hakurouken
Youmu wields both of the swords in shooters, but not in Immaterial and Missing Power. In Scarlet Weather Rhapsody, she does wield both, but only in one spellcard and an alternate special attack. And in Touhou Hisoutensoku the Hakurouken can be use there. Many fans wonder why she does not use both of the weapons at once more often.