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Fund Quantum Mechanics Lect &amp; HW Solutions 80

# Fund Quantum Mechanics Lect &amp; HW Solutions 80 - 62...

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62 CHAPTER 5. MULTIPLE-PARTICLE SYSTEMS vice-versa. But there is still almost no probability of finding both protons in the first quadrant, both near the right proton. Nor are you likely to find them in the third quadrant, both near the left proton. If you average the first two states antisymmetrically, you get the fourth picture. In the antisymmetric combination, the wave function is zero on the symmetry line between the blobs. You see that the states are really different when looked at in the full six-dimensional space. 5.2.4.2 Solution hmold-b Question: Based on the previous question, how would you think the probability density n ( z ) would look on the axis through the nuclei, again ignoring the existence of positions beyond the axis? Answer: For any state, the probability of finding electron 1 near a given z , regardless of where electron 2 is, is found by setting z 1 equal to z and integrating over all possible positions z 2 for electron 2. For the two-dimensional state ψ l ψ r shown in the left column of figure 5.2, you are
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