Write the normalized form of the ground state wavefunction of the harmonic oscillator in terms of the variable y and the parameter α. (a) Write the integral you would need to evaluate to find the mean displacement <y>, and then use a symmetry argument to explain why this integral is equal to 0. (b) Calculate <y2> (the necessary integral will be found in the Resource section). (c) Repeat the process for the first excited state.

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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.