(A) the function is an eigenfunction with eigenvalue Physical Chemistry (I) First Quiz

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1 96- Physcl Chmstry (I) Frst Quz lctron rst mss m klogrm, Plnck constnt h oul scon Sp of lght c. 8 m/s, lctron volt V.6-9 oul. Th functon F() C[cos()+sn()] s n gnfuncton of /. Th gnvlu s (A) C (B) (C) - (D) C ().. In quntum mchncs, th msurmnts of two ffrnt physcl proprts r rprsnt by th oprtors  n Ô. It s possbl to know, ctly n smultnously, th vlus for both of ths msur quntts only f th (A) oprtors  n Ô not commut. (B) [Â,Ô] ÂÔ+ÔÂ. (C) gnvlus for both oprtor  n Ô r rl numbrs. (D) oprtors  n Ô r both Hrmtn. () Non of th bov.. Whch sttmnts bout wv functon n th followng r not corrct? (A) Sngl-vlus. (B) Th bsolut vlu squr s proportonl to th probblty nsty. (C) Fnt vrywhr. (D) Postv vrywhr. () Contnuous vrywhr. 4. Whch on s th vnc tht s supportng th ntur of lght s wv? (A) Photolctrc ffct. (B) Blckboy rton. (C) Ht cpcty of sol n low tmprtur. (D) Dffrcton. () ght cn trvl wthout mum. 5. Whch sttmnt s not corrct? (A) Th wv functon for systm of ntrst s on of th gnfunctons of th systm. (B) Wv functons corrsponng to ffrnt nrgs r orthogonl. (C) Msurbl physcl proprts must b rl n not compl. Th corrsponng oprtors ll blong to th clss of Hrmtn oprtors. (D) For ny wll-bhv functons F n F, hrmtn oprtor  stsfs F ÂF τf (ÂF )τ. () Two functons r orthogonl f th ntgrl of thr prouct s zro. 6. For prtcl of mss m n cubcl bo hvng g of lngth, (A) th zro pont nrgy s h /8m. (B) th probblty nsty hs ts mmum vlu t th bo cntr for. (C) th gnrcy of th groun stt s. (D) hs thr nol plns. () Non of th bov s tru sttmnt. 7. Whn on oprtor wth / on th functon 6sn(4), on fns tht (A) th functon s n gnfuncton wth gnvlu -96.

2 96- Physcl Chmstry (I) Frst Quz (B) th functon s n gnfuncton wth gnvlu 6. (C) th functon s n gnfuncton wth gnvlu -6. (D) th functon s not n gnfuncton. () Non of th bov s tru sttmnt. 8. Wht s th numbr of nos of th hrmonc osclltor wvfuncton wth v 4? (A) (B) (C) (D) 4 () Wht s th wvlngth of lctrons tht hv bn cclrt from rst through potntl ffrnc of 4 kv?. Normlz th functon of r. A usful ntgrl: n n+ n!/.. Th vrg vlu of rus of th stnc of n lctron from th nuclus s gvn by < r > rˆ τ. Us th normlz wv functon n th bov quston to clcult vrg rus.. Confrm tht th oprtor / s hrmtn.. A prtcl s n stt scrb by th wvfuncton ( ) ( / ) / 4, whr s constnt n -. Vrfy tht th vlu of th prouct p s consstnt wth th prctons from th uncrtnty prncpl. 4. stmt typcl nuclr ctton nrgy by clcultng th frst ctton nrgy of proton confn to squr wll wth lngth qul to th mtr of nuclus ( ppromtly fm). 5. Clcult th zro-pont nrgy of hrmonc osclltor consstng of prtcl of mss. -6 kg n forc constnt 55 N m Wht s th pctton vlus of for prtcl n th stt n n prtcl-n--bo systm wth rng from / to /. 7. Wht s th pctton vlu of p for prtcl n th stt n n prtcl-n--bo systm wth rng from / to /. 8. For prtcl n cubc bo. Wht s th gnrcy of th lvl tht hs n nrgy thr tms tht of th lowst lvl. 9. Th work functon for mtllc csum s.4 V. Clcult th kntc nrgy n th sp of th lctrons ct lght of wvlngth 7 nm.. Clcult th Brogl wvlngth of mss of. g trvllng t. cm/s.

3 96- Physcl Chmstry (I) Frst Quz 參考解答. (B). (). (D) 4. (D) 5. (A) 6. (A) 7. (C) 8. (D) 9. P mk P mv k λ V h m k mv J S kg J 6. m. N r τ τ r snθrθφ r N r r sn θθ θ N ( ) / r N N / ( ˆ ). r rˆτ rτ r r r sn θθ φ 6 4 ( )

4 96- Physcl Chmstry (I) Frst Quz 4. show tht '' ' ' ' ' [ ' " ] ". Uncrtnly prncpl P ΔP ˆ { P P } / Δ { } Pˆ ( ) ( / ) / / 4 / ( / ) ˆ / / ( / ) ( / ) ( / ) / / 4 / ( ) / 4 ( ) / 4 P ( + 4 ) / 4 / 4 / / 4 ( ) / ( ) / / / / ( ) / ( )

5 96- Physcl Chmstry (I) Frst Quz 5 P / 4 / 4 ( ) / ( ) / 4 / P ( ) / / P / / 4. + n+ n h ( n ) 8m 4 ( 6.66 J s) 9.84 J.64GV kg m 5. v v + w / k w v,, m w k m / Js.55Nm. 6 kg / 4. J 6. / ( ) sn n n n / / ˆ / / sn / / cos cos ( / ) / / / / cos

6 96- Physcl Chmstry (I) Frst Quz 6 / / / sn + / / / sn 4 cos / / 7. P / / n Pˆ ( ) sn n / n Pˆ / / / P sn cos / / sn cos / 8. h ( ) n + n + n 8m h lowst lvl : 8m (,n,n ) (,, ),(,, ),(,, ) n Th gnrcy s hc 6.66 J s m / s 9 φ + k k mv hv φ φ.4.6 J 7 λ 7 m 5.88 < φ 所以無法逐出 -. λ h p h mv J s. kg. m / s m