%PDF-1.4 5 0 obj << /S /GoTo /D (section.1) >> endobj 8 0 obj ( Motivation. ) endobj 9 0 obj << /S /GoTo /D (section.2) >> endobj 12 0 obj ( Problem 1. Separation of variables. ) endobj 13 0 obj << /S /GoTo /D (subsection.2.1) >> endobj 16 0 obj ( Time independent equation. ) endobj 17 0 obj << /S /GoTo /D (subsection.2.2) >> endobj 20 0 obj ( Constant potential. ) endobj 21 0 obj << /S /GoTo /D (subsection.2.3) >> endobj 24 0 obj ( General solution. ) endobj 25 0 obj << /S /GoTo /D (section.3) >> endobj 28 0 obj ( Problem 2. Probabilities for a polynomial wavefunction. ) endobj 29 0 obj << /S /GoTo /D (subsection.3.1) >> endobj 32 0 obj ( normalize it. ) endobj 33 0 obj << /S /GoTo /D (subsection.3.2) >> endobj 36 0 obj ( definite integral of probablility. ) endobj 37 0 obj << /S /GoTo /D (section.4) >> endobj 40 0 obj ( Inverse first order wave function. ) endobj 41 0 obj << /S /GoTo /D (subsection.4.1) >> endobj 44 0 obj ( normalization. ) endobj 45 0 obj << /S /GoTo /D (subsection.4.2) >> endobj 48 0 obj ( probablility in a range. ) endobj 49 0 obj << /S /GoTo /D (subsection.4.3) >> endobj 52 0 obj ( Probability current. ) endobj 53 0 obj << /S /GoTo /D (subsection.4.4) >> endobj 56 0 obj ( expectation values. ) endobj 57 0 obj << /S /GoTo /D (subsubsection.4.4.1) >> endobj 60 0 obj ( position ) endobj 61 0 obj << /S /GoTo /D (subsubsection.4.4.2) >> endobj 64 0 obj ( momentum ) endobj 65 0 obj << /S /GoTo /D (section.5) >> endobj 68 0 obj ( Problem 4. ) endobj 69 0 obj << /S /GoTo /D (subsection.5.1) >> endobj 72 0 obj ( Second order pole contour integral. ) endobj 73 0 obj << /S /GoTo /D (subsection.5.2) >> endobj 76 0 obj ( normalize. ) endobj 77 0 obj << /S /GoTo /D (subsection.5.3) >> endobj 80 0 obj ( expectation and variance values. ) endobj 81 0 obj << /S /GoTo /D (section.6) >> endobj 84 0 obj ( Problem 5. ) endobj 85 0 obj << /S /GoTo /D (section.7) >> endobj 88 0 obj ( Problem 6. Is X operator Hermitian. ) endobj 89 0 obj << /S /GoTo /D (section.8) >> endobj 92 0 obj ( Problem 7. A current calculation. ) endobj 93 0 obj << /S /GoTo /D (section.9) >> endobj 96 0 obj ( Problem 8. ) endobj 97 0 obj << /S /GoTo /D (subsection.9.1) >> endobj 100 0 obj ( Is it normalized? ) endobj 101 0 obj << /S /GoTo /D (subsection.9.2) >> endobj 104 0 obj ( What are the values of the energy? ) endobj 105 0 obj << /S /GoTo /D (subsection.9.3) >> endobj 108 0 obj ( expectation of position ) endobj 109 0 obj << /S /GoTo /D (subsection.9.4) >> endobj 112 0 obj ( expectation of momentum ) endobj 113 0 obj << /S /GoTo /D [114 0 R /Fit ] >> endobj 116 0 obj << /Length 1428 /Filter /FlateDecode >> stream xݙn6~ -5@N16m 4^hPt*tFj4nϑx#Qc'GR$G2Re_#q"ADup2+eBM@K'm]_=~$ Q"xv}#Z4Vt STms_o['|fL$gYA D7c_157VmBM m L o֘ТmۏV82T j c6#8:_]}~