The schwarz inequality says that for any two kets v) and w) in a complex inner product space, viw)< ivi|w\, where the norm is defined by |v = (v|v). the proof is given on page 17 of shankar; write it out and find under what circumstances equality holds. use this to prove the triangle inequality for the norm of |v + w) = |v) + |w): and show that equality holds if and only if |w) = a|v) where a is a non-negative real number. hint: start with |v + w2, and use the property of complex numbers re(z)

The force acting on a beam was measured under the same operating conditions and a sample of 5 data points was collected. this process was repeated by 3 observers. the pooled standard deviations of these 3 data sets was 1.21. determine the true mean force using all pooled data (with a 95% probability). the result should look like this: true mean = mean +/- margin of error

The energy of a photon was found to be 3.38 × 10–19 j. planck’s constant is 6.63 × 10–34 j • s. which color of light corresponds to this photon?

1.)the isotope cobalt-60 has a nuclear mass of 59.933820 u calculate the mass defect of cobalt-60 using the following information. mass of proton: 1.007825 u mass of neutron: 1.008665 u 1 u = 931.5 mev 2.)the isotope cobalt-60 has a nuclear mass of 59.933820 u calculate the binding energy of cobalt-60 using the following information. mass of proton: 1.007825 u mass of neutron: 1.008665 u 1 u = 931.5 mev 3.)the isotope cobalt-60 has a nuclear mass of 59.933820 u calculate the binding energy per nucleon of cobalt-60 using the following information. mass of proton: 1.007825 u mass of neutron: 1.008665 u 1 u = 931.5 mev