| Most friendships die a natural death: people move, change jobs, or start different stages of life. Other friendships, however, end unexpectedly. When a friendship is over and you don't understand why, it can be especially painful. Sometimes a friend ends your relationship without telling you why. The loss of friendship might be worthreflecting on. Knowing when a friendship is over and why it ends may help you build stronger friendships in the future. ●See if you can find a problem.When a friendship is over, examine your relationship. Perhaps you remember your friend complaining that you're always late. Maybe you seldom return your friends' phone calls. When afriend ends your relationship, try to find out the reasons why the friendship is over. ●Write a letter to your friend.Express your feeling about the friendship. Do you miss seeing them？ Do you have any regrets (遗憾)？ Would you act differently if you were still friends？ Make it an honest communication(交流)． ●Express your feelings of hurt or anger.Write or talk about how you feel in a letter. When a friendship is over, it's important to communicate exactly how hurt you feel,and why. Write until you have nothing left to say. When a friend ends your relationship, you do have the right to express yourself. ●Communicate that you are open to picking up the friendship.When afriendship is over and you want to reconnect (再接合) some day, send Christmas, or birthday cards. Say hi and send greetings through mutual (共有的) friends. When a friendship is over, don't give up until you're ready. ●Decide to make your present friendsbips better.An adviser once told me that simply talking about your relationship strengthens your relationship. Talk to your present friends. Are they happy with your friendship？ If a friend ends your relationship, learn something from it. | 
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and the Hilbert space
. The operator
is a self-adjoint operator.
