{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Fund Quantum Mechanics Lect &amp; HW Solutions 32

# Fund Quantum Mechanics Lect &amp; HW Solutions 32 - 14...

This preview shows page 1. Sign up to view the full content.

14 CHAPTER 2. MATHEMATICAL PREREQUISITES (cos 45 , sin 45 ). The dot product of (cos 45 , sin 45 ) and (cos 45 , sin 45 ) is cos 2 45 sin 2 45 . That is zero, because cos 45 = sin 45 , so the two eigenvectors are orthogonal. In linear algebra, you would write the relationship vectorr 2 = Avectorr out as: parenleftBigg x 2 y 2 parenrightBigg = parenleftBigg 1 1 1 1 parenrightBiggparenleftBigg x y parenrightBigg = parenleftBigg x + y x + y parenrightBigg 2.6.3 Solution herm-c Question: Show that the operator hatwide 2 is a Hermitian operator, but hatwide i is not. Answer: By definition, hatwide 2 corresponds to multiplying by 2, so hatwide 2 g is simply the function 2 g . Now write the inner product ( f | 2 g ) and see whether it is the same as ( 2 f | g ) for any f and g : ( f | hatwide 2 g ) = integraldisplay all x f 2 g d x = integraldisplay all x (2 f ) g d x = ( hatwide 2 f | g ) since the complex conjugate does not affect a real number like 2. So hatwide 2 is indeed Hermitian. On the other hand, ( f | hatwide i g ) = integraldisplay all x f i g d x = integraldisplay all x (i f ) g d x = −( hatwide i f | g ) so hatwide i is not Hermitian. An operator like
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online