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1- Consider a state |w) = lø1)-l2)+163) which is given in terms of three orthonormal vectors ø1), lø2) and |ø3) of an operator  such that Âløn) = 2n|Øn). Find the expectation value of A for the state w). 2- (a) Using [X, P] = ih, show that [X², P] = 2ihX and [ÂÂ, P²] = 2ih P. (b) Show that [X2, P²] = 2ih(ih +2PÂX). %3D

1- Consider a state |w) = lø1)-l2)+163) which is given in terms of three orthonormal vectors ø1), lø2) and |ø3) of an operator  such that Âløn) = 2n|Øn). Find the expectation value of A for the state w). 2- (a) Using [X, P] = ih, show that [X², P] = 2ihX and [ÂÂ, P²] = 2ih P. (b) Show that [X2, P²] = 2ih(ih +2PÂX). %3D

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1- Consider a state |w) = lø1) -lø2)+103) which is given in terms of three orthonormal vectors lø1), lø2) and |03) of an operator Ä such that Ä|øn) = 2n|Pn). Find the expectation value of Ä for the state |w). 2- (a) Using [X, P] = ih, show that [ÂY², P] = 2ihX and [X, P²]= 2ihP. (b) Show that [X2, ê²] = 2ih(ih +2PX).
Transcribed Image Text:1- Consider a state |w) = lø1) -lø2)+103) which is given in terms of three orthonormal vectors lø1), lø2) and |03) of an operator Ä such that Ä|øn) = 2n|Pn). Find the expectation value of Ä for the state |w). 2- (a) Using [X, P] = ih, show that [ÂY², P] = 2ihX and [X, P²]= 2ihP. (b) Show that [X2, ê²] = 2ih(ih +2PX).
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