4. Very cold neutrons can be generated that fall in the gravitational field and bounce back from a surface (see Nesvizhevsky V. V. et al., Nature, 415, 297 (2002)). Using the Bohr-Sommerfeld quantization rule (Eq.2.10 in the notes) show that the energy levels of a bouncing neutron are: En=mg (9n²h? /32 m2 g) You'll need the identity: V1-x dx = 2/3 %3D The mass of the neutron is: m =1,675×10 24g; the gravitational acceleration: g= 10 cm/sec?, Compute the first energy levels and compare them with the experiment reported in the Nature paper.
4. Very cold neutrons can be generated that fall in the gravitational field and bounce back from a surface (see Nesvizhevsky V. V. et al., Nature, 415, 297 (2002)). Using the Bohr-Sommerfeld quantization rule (Eq.2.10 in the notes) show that the energy levels of a bouncing neutron are: En=mg (9n²h? /32 m2 g) You'll need the identity: V1-x dx = 2/3 %3D The mass of the neutron is: m =1,675×10 24g; the gravitational acceleration: g= 10 cm/sec?, Compute the first energy levels and compare them with the experiment reported in the Nature paper.
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Transcribed Image Text:4. Very cold neutrons can be generated that fall in the gravitational field and bounce back
from a surface (see Nesvizhevsky V. V. et al., Nature, 415, 297 (2002)). Using the
Bohr-Sommerfeld quantization rule (Eq.2.10 in the notes) show that the energy levels
of a bouncing neutron are:
E =mg (9n h /32 m² g)
1/3
%3D
You'll need the identity: V1-x dx 2/3
%3D
-24
The mass of the neutron is: m 1,675x102g; the gravitational acceleration:g
10 cm/sec?. Compute the first energy levels and compare them with the experiment
reported in the Nature paper.
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