Stationary electron broglie wavelength

• roboticmehdi
In summary, de broglie's formulation states that the wavelength of a particle is inversely proportional to its momentum. When the momentum of a particle is high, it exhibits less wave-like behavior. However, for an electron in a stationary state with zero velocity, its wavelength becomes infinite. This does not mean the electron disappears, but rather that its position becomes infinitely uncertain according to the uncertainty principle. This also applies to any speed, not just zero.
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?

roboticmehdi said:
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?

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 $\Delta v \propto \frac{\hbar}{m r}$.

sergiokapone said:
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 $\Delta v \propto \frac{\hbar}{m r}$.

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?

roboticmehdi said:
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?

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

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

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 ?

roboticmehdi said:
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 ?

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.

sergiokapone said:
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.

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=∞ ?

roboticmehdi said:
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=∞ ?

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

hi roboticmehdi! hi sergiokapone!
sergiokapone said:
A consequence of λ=∞ would be that the uncertainty in position becomes infinite. And that's all.

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

tiny-tim said:
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

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.

tiny-tim said:
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

i know those things about wave but i don't 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...

What is the stationary electron Broglie wavelength?

The stationary electron Broglie wavelength is a theoretical concept in quantum mechanics that describes the wavelength of an electron in a stationary state, or a state where the electron's energy does not change over time.

How is the stationary electron Broglie wavelength calculated?

The stationary electron Broglie wavelength is calculated using the formula λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the electron.

What is the significance of the stationary electron Broglie wavelength?

The stationary electron Broglie wavelength is significant because it helps us understand the wave-like behavior of electrons in quantum mechanics. It also has practical applications in fields such as electron microscopy and semiconductor technology.

How does the stationary electron Broglie wavelength differ from the de Broglie wavelength?

The stationary electron Broglie wavelength is a specific case of the de Broglie wavelength, which describes the wavelength of any moving particle. The stationary electron Broglie wavelength only applies to electrons in a stationary state, while the de Broglie wavelength applies to all particles.

Can the stationary electron Broglie wavelength be observed in experiments?

No, the stationary electron Broglie wavelength cannot be directly observed in experiments because it is a theoretical concept. However, the effects of the stationary electron Broglie wavelength can be observed in experiments, such as in the diffraction patterns produced by electrons in an electron microscope.

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