The wave function for the ground state of the harmonic oscillator is %0 (2) = Ce-mw/(2A)|z² where C is an arbitrary constant, ħ is Planck's constant divided by 27, m is the mass of the particle, w = √k/m, and k is the "spring constant" for the harmonic oscillator. Normalize this wave function. What is the (positive) value of C once this wave function is normalized? You will need the formula -az² Express your answer in terms of w, m, h, and T. ► View Available Hint(s) C= IT ΑΣΦ Xh √x √x x IXI X.10n

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Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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The wave function for the ground state of the harmonic
oscillator is
Vo(x) = Ce-[mw/(2ħ)]x²
where C is an arbitrary constant, ħ is Planck's constant
divided by 2π, m is the mass of the particle,
W = ✓k/m, and k is the "spring constant" for the
harmonic oscillator.
Part A
Normalize this wave function. What is the (positive) value of C once this wave function is normalized? You will need the formula
Se
-∞
Express your answer in terms of w, m, ħ, and T.
► View Available Hint(s)
C =
17 ΑΣΦ
xa
Xh
عات
a
√x vx
18
X>
IXI
-ax²
X.10n
X
=
?
wwwwwwwwww
√.
a
Transcribed Image Text:The wave function for the ground state of the harmonic oscillator is Vo(x) = Ce-[mw/(2ħ)]x² where C is an arbitrary constant, ħ is Planck's constant divided by 2π, m is the mass of the particle, W = ✓k/m, and k is the "spring constant" for the harmonic oscillator. Part A Normalize this wave function. What is the (positive) value of C once this wave function is normalized? You will need the formula Se -∞ Express your answer in terms of w, m, ħ, and T. ► View Available Hint(s) C = 17 ΑΣΦ xa Xh عات a √x vx 18 X> IXI -ax² X.10n X = ? wwwwwwwwww √. a
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