Q7CQ We say that the ground state for... [FREE SOLUTION]

Chapter 5: Q7CQ (page 186)

We say that the ground state for the particle in a box has nonzero energy. What goes wrong with $唯$ in equation 5.16 if n = 0 ?

Short Answer

Expert verified

If n = 0 in equation of $唯_{n} (x) = \sqrt{\frac{2}{L}} \sin (\frac{苍蟿蟿虫}{L})$ , this would make locating our particle difficult, meaning that it no longer exists.

Step by step solution

Calculating Ψn(x) for n=0

The equation is given $唯 = 5.16$ wheren n = 0

The equation in question says that for 0<x<L

$唯_{n} (x) = \sqrt{\frac{2}{L}} \sin (\frac{苍蟿蟿虫}{L})$

If n = 0 ,this equation gives us $唯_{n} = 0$ . This would make it impossible to locate our particle, implying that the particle no longer exists.

Conclusion

If a square well potential had a ground state with zero energy, it would suggest that the particle would be at rest inside the square well (due to its zero energy), which would obviously violate Heisenberg's uncertainty principle.

Therefore, It is not possible to locate the particle if n = 0

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91影视

We say that the ground state for the particle in a box has nonzero energy. What goes wrong with $唯$ in equation 5.16 if n = 0 ?

Short Answer

Step by step solution

Calculating Ψn(x) for n=0

Conclusion

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91影视

We say that the ground state for the particle in a box has nonzero energy. What goes wrong with 唯in equation 5.16 if n = 0 ?

Short Answer

Step by step solution

Calculating Ψn(x) for n=0

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Scientific Method Physics

Fundamentals of Physics

Classical Mechanics

Electromagnetism

Physical Quantities And Units

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.

We say that the ground state for the particle in a box has nonzero energy. What goes wrong with $唯$ in equation 5.16 if n = 0 ?