Q4P Show that聽螛=AIn[tan(胃2)]聽sat... [FREE SOLUTION]

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Introduction to Quantum Mechanics

David J. Griffiths

Physics

2nd Edition 路 469 pages

ISBN: 9780131118928

Chapter 4: Q4P (page 139)

Show that $螛 = A I n [t a n (\frac{胃}{2})]$ satisfies the $胃$ equation (Equation 4.25), for l = m = 0. This is the unacceptable "second solution" -- whats wrong with it?

Short Answer

Expert verified

$螛 (胃) = A I n [\tan \frac{胃}{2}]$ does satisfy the equation but this is the unacceptable second solution since $螛$ blows up at $胃 = 0$ and at $胃 = 蟺$

Step by step solution

Define the Schrödinger equation

A differential equation describes matter in quantum mechanics in terms of the wave-like properties of particles in a field. Its answer is related to a particle's probability density in space and time.

Calculation

We need to show that,

$螛 (胃) = A I n [\tan \frac{胃}{2}]$

Satisfies the equation

$\sin (胃) \frac{d}{d 胃} (\sin (胃) \frac{d 螛}{d 胃} + [I (I + 1) \sin^{2} (胃) - m^{2}] 螛 = 0$

So now take the derivative then we get,

$\frac{d 螛}{d 胃} = \frac{A}{\tan (\frac{胃}{2})} \frac{1}{2} \sec^{2} (\frac{胃}{2}) \frac{d 螛}{d 胃} = \frac{A}{2} \frac{1}{\sin (\frac{胃}{2}) \cos (\frac{胃}{2})} = \frac{A}{\sin 胃}$

Therefore,

$\frac{d}{d 胃} (\sin 胃 \frac{d 螛}{d 胃}) = \frac{d}{d 胃} A = 0$

Then, we get,

role="math" localid="1656064432888" $螛 (0) = A I n (0) = A (- 鈭�) 螛 (蟺) = A I n (\tan \frac{蟺}{2}) = A I n (- 鈭�) = A (鈭�)$

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91影视

Show that $螛 = A I n [t a n (\frac{胃}{2})]$ satisfies the $胃$ equation (Equation 4.25), for l = m = 0. This is the unacceptable "second solution" -- whats wrong with it?

Short Answer

Step by step solution

Define the Schrödinger equation

Calculation

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91影视

Show that螛=AIn[tan(胃2)]satisfies the 胃equation (Equation 4.25), for l = m = 0. This is the unacceptable "second solution" -- whats wrong with it?

Short Answer

Step by step solution

Define the Schrödinger equation

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Particle Model of Matter

Astrophysics

Fluids

Thermodynamics

Turning Points in Physics

Further Mechanics and Thermal Physics

Study anywhere. Anytime. Across all devices.

Show that $螛 = A I n [t a n (\frac{胃}{2})]$ satisfies the $胃$ equation (Equation 4.25), for l = m = 0. This is the unacceptable "second solution" -- whats wrong with it?