Solve the following questions relating to the Harmonic Oscillator.
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Solve the following questions relating to the Harmonic Oscillator.
![d.
e.
Confirm that the state (x) obeys the uncertainty relation for
potential and kinetic energy given by σTσv ≥ |(4₁(x) |⁄2 [΂Ñ]| 4(x))|.
2i
The Virial Theorem applied to the Harmonic Oscillator demands that
the average kinetic energy plus the average potential energy is equal to the total
energy. Confirm that the Virial Theorm holds for the ground state of the
Harmonic Oscillator if you equate the average potential energy to (V) and the
average kinetic energy to (T).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdcd1876a-e36d-434d-a45b-4f04f4162f11%2F898086e2-b6fd-4386-ae6e-a7c065b8e080%2F5y4a8su_processed.png&w=3840&q=75)
Transcribed Image Text:d.
e.
Confirm that the state (x) obeys the uncertainty relation for
potential and kinetic energy given by σTσv ≥ |(4₁(x) |⁄2 [΂Ñ]| 4(x))|.
2i
The Virial Theorem applied to the Harmonic Oscillator demands that
the average kinetic energy plus the average potential energy is equal to the total
energy. Confirm that the Virial Theorm holds for the ground state of the
Harmonic Oscillator if you equate the average potential energy to (V) and the
average kinetic energy to (T).
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
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