The wave functions p. and d are linear combinations of the spherical harmonic functions, which are eigenfunctions of the operators Ĥ, i², and Î, for rotation in three dimensions. The combinations have been chosen to yield real functions. ▾ Part A Are these functions still eigenfunctions of 1₂? Answer this question by applying the operator to the functions. Match the items in the left column to the appropriate blanks in the sentences and the equations on the right. Make certain each sentence and equation is complete before submitting your answer. 3 V4T sin 15 √4π 4 V 15T 15п 4 V 3T 3π COS 1₂P₂-ih 8 8p o. This shows that pz 8 86 izdzz -ih- 0 0 0 =ih an eigenfunction of 1₂. p. This shows that das Reset Help 0 an eigenfunction of 1₂.

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Techniques and applications of quantum theory

Quantum theory, often known as quantum physics, is the foundation of modern physics and encompasses the nature and behavior of matter and energy at the atomic and molecular levels. As the exact nature and behavior of atomic and subatomic particles are impossible to determine, the laws of classical physics do not apply to this discipline. As a result, quantum field theory is primarily based on assumptions and probabilities.