# Stationary electron broglie wavelength

1. Mar 11, 2012

### roboticmehdi

de broglie's formulation:

λ=h/(mv)

the more the momentum of a particle, the less wave-like behaviour it shows. But what if we have electron which is stationary, i.e. zero speed, according to formula λ becomes ∞. What does this mean? Does the electron disappear?

2. Mar 11, 2012

### sergiokapone

Why did you decide that an electron in a stationary state has zero velocity? This is an incorrect statement. Even from Bohr's theory implies that in stationary state we have a nonzero angular momentum, and as a result nonzero velocity.
From the viewpoint of the Schrodinger equation, the orbital angular momentum of the hydrogeh-like atom in the ground state is zero. But this does not mean that the electron velocity is zero due to uncertainty principle. Uncertainty in the position of the electron is of the order size of an atom $r$ , thus uncertainty in the electron velocity is equal to $\Delta v \propto \frac{\hbar}{m r}$.

3. Mar 11, 2012

### roboticmehdi

But I am not talking about an electron in atom. Of course there an electron can not be stationary. Imagine you fire some electrons from electron gun in space and then you accelerate until you reach their speed ( this is possible since they move at lower speed than speed of light ). what would then happen? the wavelength becomes infinite? what happens to electron then?

4. Mar 11, 2012

### sergiokapone

Electron is in a ground state in atom just the stationary! If you acсelerate electron, its wavelength decreases, tends to zero (not to infinity).

5. Mar 11, 2012

### roboticmehdi

Forget about the atom. You fire some electrons, then you catch up with them. Relative to you their speed becomes ZERO. λ=h/(m*0)=∞ do you agree now ?

6. Mar 11, 2012

### sergiokapone

Ok, if you go with the electron velocity, really, you find it velocity to be zero, but you will never know where it is, due to uncertainty principle. $\lambda \to \infty$ of this says.

7. Mar 11, 2012

### roboticmehdi

I don't care about its position. I just want to know what happens when the wavelength becomes infinite. what happens to electron ? what are the consequences of λ=∞ ?

8. Mar 11, 2012

### sergiokapone

And none of it will not happen. A consequence of λ=∞ would be that the uncertainty in position becomes infinite. And that's all.

9. Mar 11, 2012

### tiny-tim

hi roboticmehdi! hi sergiokapone!
i was thinking of giving this answer too, but the problem is that the same argument applies at any speed …

if we know the velocity is exactly v, then its position is again infinitely uncertain

the wavelength is simply the distance it travels during a "phase rotation" of 2π …

watch something follow a sine wave … now keep the amplitude the same and reduce the (horizontal) speed to 0 … it simply goes up and down without moving horizontally … it travels 0 during a "phase rotation" of 2π

10. Mar 11, 2012

### roboticmehdi

Yeah. The uncertainty principle is about Δv and Δx, not about v. you could have infinite uncertainty in position in any speed not just 0 m/s. what i am asking is, what happens to electron at zero speed, what are the consequences of λ being equal to infinity.

11. Mar 11, 2012

### roboticmehdi

i know those things about wave but i dont think that electron is moving up and down just like that. it that would be the case the the up and down motion itself would generate another wave and that would generate another one and etc...