PLEASE ANSWER ALL THESE QUESTIONS ▬▬M8.PCWAW19.5=UHomeCutCopyFormat PainterClipboardFilePaste| +15° |·14° |·13· |·12·1·11·1·10·|·9·1·8·1·7·1·6·1·5·1·4·1·3·1·2·1·1······20Insertall04:00 PM2022-06-18 Page: 1 of 1 Words: 3Page LayoutReferencesCalibri (Body) 11TTΑ Α΄BIUabe X, X² ATFontI U abe X₂ X³Document2 - Microsoft Word (Product Activation Failed)ReviewViewB-B-S ## TAaBbCcDc AaBbCcDc AaBbC AaBbCc AaBl AaBbCclabNormalNo Spaci... Heading 1Heading 2TitleSubtitleFParagraphGStyles··2 · 1 · 1 ·|·|·|·1·1·2·1·3·1·4·1·5·1· 6 · 1 · 7 · 1 · 8 · 1 ·9·1·10° | ·11·|··12·|·13·|··14° | ・15·| ·|\_\ ·| ·17·|*18* ||QUANTUM PHYSICS QUESTIONConsider the dimensionless harmonic oscillator HamiltonianÂ =-=-²²+½-X²,with P =ddx(a) Show that the two wave functions yo(x) = e-x²/2 and y/1(x) = xe-x²/2 are eigenfunc-tions of Ĥ with eigenvalues 1/2 and 3/2, respectively.(b) Find the value of the coefficient a such that w2(x) = (1 + ax²) e-x²/2 is orthogonal toyo(x). Then show that y2(x) is an eigenfunction of Ĥ with eigenvalue 5/2.MailingsAalAaААChangeStylesG■ ¥良酒 ≡ 80%Findчасac ReplaceSelect -Editing@?184V+

Answered: Image /qna-images/answer/894208ce-bf0b-4ecc-a26c-a6483ab30aa3.jpg

QUANTUM PHYSICS QUESTION Consider the dimensionless harmonic oscillator Hamiltonian with P (a) Show that the two wave functions yo(x) = ex²2 and 1(x) = xe-²/2 are eigenfunc- tions of Ĥ with eigenvalues 1/2 and 3/2, respectively. (b) Find the value of the coefficient a such that y2(x) = (1 + ax²)e-²/2 is orthogonal to wo(x). Then show that w2(x) is an eigenfunction of Ĥ with eigenvalue 5/2.

QUANTUM PHYSICS QUESTION Consider the dimensionless harmonic oscillator Hamiltonian with P (a) Show that the two wave functions yo(x) = ex²2 and 1(x) = xe-²/2 are eigenfunc- tions of Ĥ with eigenvalues 1/2 and 3/2, respectively. (b) Find the value of the coefficient a such that y2(x) = (1 + ax²)e-²/2 is orthogonal to wo(x). Then show that w2(x) is an eigenfunction of Ĥ with eigenvalue 5/2.