Wavelength of a Tennis Ball at 0 Velocity

[Thejas15101998]

In the De Broglie equation : λ = h / (m v) what happens when the velocity of an object is zero? I see that we get ∞ wavelength . It is not making any sense to me. Could anyone please help me. Let's take the object to be a tennis ball say.

 

[Vanadium 50]

Why don't you put some numbers in. For v, uise one micron per century. That's pretty close to zero.

 

[Thejas15101998]

Why don't you put some numbers in. For v, uise one micron per century. That's pretty close to zero.

why not zero itself for velocity? What is the significance of infinite wavelength? what does it convey?

 

[Vanadium 50]

I was trying to teach you something, But never mind.

 

[vanhees71]

De Broglie's theory is outdated for about 91 years now. Why do you bother with it. The right place to start is non-relativistic quantum mechanics, which you can formulate as "wave mechanics" a la Schrödinger. Then think about the question, whether there is a state represented by a momentum eigenvector. Note that wave functions can only represent true states if they are square integrable, i.e., for which you can normalize the wave function such that
$$\langle \psi|\psi \rangle=\int_{\mathbb{R}^3} \mathrm{d}^3 \vec{x} |\psi(\vec{x})|^2=1.$$

 

[Demystifier]

In the De Broglie equation : λ = h / (m v) what happens when the velocity of an object is zero? I see that we get ∞ wavelength . It is not making any sense to me. Could anyone please help me. Let's take the object to be a tennis ball say.

The De Broglie relation makes sense only when combined with Heisenberg uncertainty principle. If velocity v is known with certainty (be it 0 or any other definite value), then position is totally unknown. The infinite wavelength (or any other well defined wavelength) expresses the fact that the particle can be found anywhere.

In a realistic situation the velocity is never known with absolute precision, and consequently the wavelength is also not known with absolute precision.