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This chapter gives a brief introduction to quantum mechanics. Quantum mechanics can be thought of roughly as the study of physics on very small length scales, although there are also certain macroscopic systems it directly applies to. The descriptor “quantum” arises because in contrast with classical mechanics, certain quantities take on only discrete values. However, some quantities still take on continuous values, as we’ll see. In quantum mechanics, particles have wavelike propertie...

This chapter gives a brief introduction to quantum mechanics. Quantum mechanics can be thought of roughly as the study of physics on very small length scales, although there are also certain macroscopic systems it directly applies to. The descriptor “quantum” arises because in contrast with classical mechanics, certain quantities take on only discrete values. However, some quantities still take on continuous values, as we’ll see. In quantum mechanics, particles have wavelike propertie...

This chapter gives a brief introduction to quantum mechanics. Quantum mechanics can be thought of roughly as the study of physics on very small length scales, although there are also certain macroscopic systems it directly applies to. The descriptor “quantum” arises because in contrast with classical mechanics, certain quantities take on only discrete values. However, some quantities still take on continuous values, as we’ll see. In quantum mechanics, particles have wavelike propertie...

In this section we’ll give a “derivation” of the Schrodinger equation. Our starting point will be the classical nonrelativistic expression for the energy of a particle, which is the sum of the kinetic and potential energies. We’ll assume as usual that the potential is a function of only x. We have E = K + V = 1 2 mv2 + V (x) = p 2 2m + V (x). (3) We’ll now invoke de Broglie’s claim that all particles can be represented as waves with frequency ω and wavenumber k, and that...

Consider the diagram below. b c Name the regions labeled a, b, c. (3 marks) a Pale blue zone b Green blue zone c Almost colourless zone

2 5 4+5 9 5 18−15 3 1 = M1 M1 A1 = − = = = 3 6 6 6 4 1 1 6 9 160+27 187 16 = 2 1 12 4 7 11 77 + = 2 77 30+539 569 187 - × = 17070 3 15 513 = 3150 630 − + = = 30 1 630 −315 = 3150 × 2. 1 2 6.458 × 10−2 2 ( ) 0.4327 2.541 + (2.311)2 = 2.541 + 2(5.307) = 2.541 + 10.61 =13.155 M1 M1 M1 A1

81x+1 + 34x = 246 34(x+1) + 34x = 246 3 4x x 34 + 34x = 246 Let 34x = y 81y +y= 246 82y=246 82 82 y=3 34x=31 x M1 M1 A

1. Evaluate; 3.45 + 2.62 (3mks) 786 x 0.007 2. The exterior angle of a rectangular polygon is an eighth of interior angle. How many sides does the regular polygon have? (3mks)

What is the place value of total value of digit 6 underlined below.. (3mks) 47,397,263,402 Ten thousands t.v= p.v x N 10000 x 6 =60,000 2. Round off the following numbers to the nearest number indicated in the brackets. (3mks) a) 473,678(100) 473700 b) 379(10) 380 c) 38,679(10,000) 40,000 3. Write the following in symbols. (2mks) a) Five billion, five million, five thousand and five. 5,005,005,005 b) Write the following in words 80,000,045, 000 (2mks) Eighty billion...