- #1
mike1000
- 271
- 20
Lets pretend there is a gun of some type that can fire electrons one at at time at a wall. The plane of the wall is oriented perpendicular to the x axis, which is to say that the wall is in the y-z plane some distance down the xaxis.
There is no intervening screen with slits in it. We are just firing an electron at a wall.
The electron is fired at the wall, at some well defined momentum in the x-direction, call it ##p_x##. I am going to assume that the momentums of the electron in the transverse directions (y,z) are also well defined but I really do not know if that is true. I think the momentum in the y and z directions, ##p_y## and ##p_z## is such that the electron actually follows a helical path to the wall, but I am not sure of that. (I will deal with that later, because if that is true, isn't the motion of the electon in the plane transverse to its direction of motion equivalent to an angular momentum about the x-axis?)
For the moment, my question is this...
Where on the wall will the electron hit? Will it hit the point where the gun is aiming? Or will it hit all over the place? If I understand correctly, if ##p_y## and ##p_z## are well defined then the position of the electron in the y and z directions is completely undefined making it equally probable that the electron can hit anywhere on that wall because the wave functions in the y and z directions should be plane sine waves.
There is no intervening screen with slits in it. We are just firing an electron at a wall.
The electron is fired at the wall, at some well defined momentum in the x-direction, call it ##p_x##. I am going to assume that the momentums of the electron in the transverse directions (y,z) are also well defined but I really do not know if that is true. I think the momentum in the y and z directions, ##p_y## and ##p_z## is such that the electron actually follows a helical path to the wall, but I am not sure of that. (I will deal with that later, because if that is true, isn't the motion of the electon in the plane transverse to its direction of motion equivalent to an angular momentum about the x-axis?)
For the moment, my question is this...
Where on the wall will the electron hit? Will it hit the point where the gun is aiming? Or will it hit all over the place? If I understand correctly, if ##p_y## and ##p_z## are well defined then the position of the electron in the y and z directions is completely undefined making it equally probable that the electron can hit anywhere on that wall because the wave functions in the y and z directions should be plane sine waves.