# ps3c - Now lets calculate the expectation value of the...

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Unformatted text preview: Now, lets calculate the expectation value of the Hamiltonian. 1 n 0 , Emu/"r“ e M (MM) l l ~00 : 403/ ch 726’ O i /‘°° ( hz : _ du e 2 0 2 We? 3777,4412 2777 2&2 3 2 a _ h /d37“ 6 (W 7‘ 7T . . 2 m m< 2 O; U 771' Now, lets find the minimum with respect to alpha gimme : —’ , Then Plugging this into (18). we get (\Ilel‘lj> : Therefore . 148. Take as a trial wave function 2 a: 77,2 (1' 771 377'Lw 2 “3 x/gmw y/g flu} 2 h, \L‘W 2 E0 g ﬁm. First calculate the normalization constant. —00 Then (\IIlTNJ) : V 38 /2 ZV/i: N,— L, 7.12 52 2m 5712232 1/4 (g) V? NOW7 lets calculate the expectation value of the kinetic energy dm 6—82 Z ( :0 oo 00 [— / dw \I/*\II : Ng/ d2? 6—25ng : N2V/Zl ﬁg d2 2m W x/‘Sm 2,2 >€ﬂﬁ\$ 00 . 2 2 [GO dm (2 - 452w2)e_28 m / “ V/E _ WW 7 2m MW <16) (l7) (l8) ...
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