update textbook

doc/BookChapters/BookProject/.gradientmethods.exerinfo

@@ -0,0 +1,95 @@
+# Information about all exercises in the file gradientmethods.do.txt.
+# The information can be loaded into a Python list of dicts by
+#
+# f = open('.gradientmethods.exerinfo', 'r')
+# exer = eval(f.read())
+#
+[{'ans_docend': '',
+  'answer': '',
+  'chapter_exercise': None,
+  'chapter_no': None,
+  'chapter_title': None,
+  'chapter_type': None,
+  'closing_remarks': '',
+  'file': None,
+  'heading': '=====',
+  'hints': [],
+  'keywords': None,
+  'label': None,
+  'no': 1,
+  'sol_docend': '',
+  'solution': '',
+  'solution_file': None,
+  'subex': [{'ans_docend': '',
+             'answer': '',
+             'file': None,
+             'hints': [],
+             'sol_docend': '',
+             'solution': '',
+             'text': 'Derive the local energy for the harmonic oscillator in '
+                     'one dimension and find its expectation value.'},
+            {'ans_docend': '',
+             'answer': '',
+             'file': None,
+             'hints': [],
+             'sol_docend': '',
+             'solution': '',
+             'text': 'Show also that the optimal value of optimal $\\alpha=1$'},
+            {'aftertext': '\n\n',
+             'ans_docend': '',
+             'answer': '',
+             'file': None,
+             'hints': [],
+             'sol_docend': '',
+             'solution': '',
+             'text': 'Repeat the above steps in two dimensions for $N$ bosons '
+                     'or electrons. What is the optimal value of $\\alpha$?'}],
+  'text': '',
+  'title': 'Find the local energy for the harmonic oscillator',
+  'type': 'Exercise',
+  'type_visible': True},
+ {'ans_docend': '',
+  'answer': '',
+  'chapter_exercise': None,
+  'chapter_no': None,
+  'chapter_title': None,
+  'chapter_type': None,
+  'closing_remarks': '',
+  'file': None,
+  'heading': '=====',
+  'hints': [],
+  'keywords': None,
+  'label': None,
+  'no': 2,
+  'sol_docend': '',
+  'solution': '',
+  'solution_file': None,
+  'subex': [{'ans_docend': '',
+             'answer': '',
+             'file': None,
+             'hints': [],
+             'sol_docend': '',
+             'solution': '',
+             'text': 'Show that \n'
+                     '!bt\n'
+                     '\\[\n'
+                     '\\bar{E}_{\\alpha} = 2\\left( \\langle '
+                     '\\frac{\\bar{\\psi}_{\\alpha}}{\\psi[\\alpha]}E_L[\\alpha]\\rangle '
+                     '-\\langle '
+                     '\\frac{\\bar{\\psi}_{\\alpha}}{\\psi[\\alpha]}\\rangle\\langle '
+                     'E_L[\\alpha] \\rangle\\right).\n'
+                     '\\]\n'
+                     '\n'
+                     '!et'},
+            {'aftertext': '\n\n\n\n',
+             'ans_docend': '',
+             'answer': '',
+             'file': None,
+             'hints': [],
+             'sol_docend': '',
+             'solution': '',
+             'text': 'Find the corresponding expression for the variance.'}],
+  'text': '',
+  'title': 'General expression for the derivative of the energy',
+  'type': 'Exercise',
+  'type_visible': True}]