What should a young man do who loves a girl but cannot marry her at present, and all impermissible means of communication between them have been cut off, yet she never leaves his memory?

It is not permissible for a young man and an unrelated young woman to engage in conversation, and you did well by cutting off communication with her. The solution for those who are in love is marriage, to extinguish the fire of passion, as the Prophet, peace and blessings be upon him, said: "We have not seen for two who love one another anything like marriage." Study or poverty are not impediments to marriage; a poor student may marry, and righteous people may assist him. If marriage is facilitated, then that is excellent. Otherwise, protect yourself by fasting and occupying your time with what is beneficial, and by keeping the company of the righteous. For the treatment of passionate love, you may refer to the fatwas related to that.