1. The following questions will relate to the Harmonic Oscillator with the following Hamiltonian in a system of natural units where k 1, μµ = 1,ħ = 1: Н = 1 d² 2 dx² With ground-state wavefunction given by: =+ Pule) = (-) + + + 4₁(x) 2 ·X²
1. The following questions will relate to the Harmonic Oscillator with the following Hamiltonian in a system of natural units where k 1, μµ = 1,ħ = 1: Н = 1 d² 2 dx² With ground-state wavefunction given by: =+ Pule) = (-) + + + 4₁(x) 2 ·X²
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Calculate the uncertainties for the following
Transcribed Image Text:1.
The following questions will relate to the Harmonic
Oscillator with the following Hamiltonian in a system of natural units where k = 1, µ =
1,ħ = 1:
Ĥ :
=
1 d² 1
2 d x² + z ²
With ground-state wavefunction given by:
Yo (x)
- G) ₁
=
x²
2
Transcribed Image Text:a.
b.
C.
Compute the uncertainty energy OE = √(E²) — (E)² for the state
(x) and report the value in natural units of energy. Does this state have a
precise energy?
Compute the uncertainty kinetic energy T = √(T²) - (T)² for the
state (x) and report the value in natural units of energy. Does this state have
a precise value of kinetic energy?
Compute the uncertainty kinetic energy σv = √√√(V²) – (V)² for the
state (x) and report the value in natural units of energy. Does this state have
a precise value of potential energy?
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