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Consider an ##N_2## molecule. Chemists say that the triple bond is due to one ##p_x - p_x## overlap, one ##p_y - p_y## overlap and one ##p_z - p_z## overlap. The x-axis (the label is not important; I’m sure you know what I mean) is clear because it’s the longitudinal axis of the molecule. But how do you know what the directions of y and z axes in the physical world are?

Also, since any linear combination of ##p_y## and ##p_z## is also a solution to Schrodinger equation, how do you know the electrons are not in this kind of state? Why must they be purely in ##p_y## or ##p_z##? (Suppose you believe the chemists are right.)

Are the electrons purely in ##p_y## and ##p_z##? ##p_y## and ##p_z## are pointing in some definite direction in space, it’s just that those definite directions are unknown to us. Or are the electrons in a linear combination of ##p_y## and ##p_z## such that their orbital looks like a cylindrical shell surrounding the x axis? (Like a toilet paper roll with uniform probability amplitude all over the curved surface.)

Also, since any linear combination of ##p_y## and ##p_z## is also a solution to Schrodinger equation, how do you know the electrons are not in this kind of state? Why must they be purely in ##p_y## or ##p_z##? (Suppose you believe the chemists are right.)

Are the electrons purely in ##p_y## and ##p_z##? ##p_y## and ##p_z## are pointing in some definite direction in space, it’s just that those definite directions are unknown to us. Or are the electrons in a linear combination of ##p_y## and ##p_z## such that their orbital looks like a cylindrical shell surrounding the x axis? (Like a toilet paper roll with uniform probability amplitude all over the curved surface.)

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