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3. A special form of the deuteron wave function $\psi_d = r^{-1}u(r)Y_{00}$ was given by Hultén as $u(r) = ce^{-\alpha r}(1 - e^{-\mu r})$, which is the exact solution of the Schrödinger equation to the Hultén potential $V(r) = V_0e^{-\mu r}\frac{1}{1 - e^{-\mu r}}$ a. Show that the normalisation is given by $c = \sqrt{2\alpha(\alpha + \mu)(2\alpha + \mu)\mu^{-1}}$. b. Determine $\alpha$, $\mu$, and $V_0$ from known quantities of the deuteron, i.e. the r.m.s. radius $r_n - r_p = 3.8$ fm and the binding energy of -2.22 MeV. Hint: Two conditions for $\alpha$, $\mu$, and $V_0$ come from the Schrödinger equations. This must be valid for all r.

          3. A special form of the deuteron wave function $\psi_d = r^{-1}u(r)Y_{00}$ was given by Hultén as
$u(r) = ce^{-\alpha r}(1 - e^{-\mu r})$, which is the exact solution of the Schrödinger equation to the
Hultén potential
$V(r) = V_0e^{-\mu r}\frac{1}{1 - e^{-\mu r}}$
a. Show that the normalisation is given by $c = \sqrt{2\alpha(\alpha + \mu)(2\alpha + \mu)\mu^{-1}}$.
b. Determine $\alpha$, $\mu$, and $V_0$ from known quantities of the deuteron, i.e. the r.m.s. radius
$r_n - r_p = 3.8$ fm and the binding energy of -2.22 MeV. Hint: Two conditions for $\alpha$, $\mu$,
and $V_0$ come from the Schrödinger equations. This must be valid for all r.

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3. A special form of the deuteron wave function = r^-1u(r)Y00 was given by Hultén as
u(r) = ce^-α r(1 - e^-μ r), which is the exact solution of the Schrödinger equation to the
Hultén potential
V(r) = V0e^-μ r(1)/(1 - e^-μ r)
a. Show that the normalisation is given by c = √(2α(α + μ)(2α + μ)μ^-1).
b. Determine α, μ, and V0 from known quantities of the deuteron, i.e. the r.m.s. radius
rn - rp = 3.8 fm and the binding energy of -2.22 MeV. Hint: Two conditions for α, μ,
and V0 come from the Schrödinger equations. This must be valid for all r.

Added by Hector N.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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The text provided appears to be a physics problem related to the deuteron wave function and the Hultén potential. The text contains mathematical equations and symbols, and it seems to be asking for the normalization of the wave function and the determination of certain parameters from known quantities of the deuteron. The text contains some typographical errors, such as missing subscripts and superscripts, incorrect mathematical symbols, and formatting issues. Additionally, there are OCR errors in the form of incorrect characters and symbols. To correct the text, the following steps can be taken: 1. Identify and correct any typographical errors, such as missing subscripts and superscripts, incorrect mathematical symbols, and formatting issues. 2. Verify the mathematical equations and symbols for accuracy and correct any errors related to the square root symbol. 3. Ensure that the entire text is properly formatted and presented in a clear, coherent manner. After these steps are completed, the text should be free from spelling, typographical, grammatical, OCR, and mathematical errors, and it should be properly formatted and presented in a clear, coherent manner.

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