Natural units Peter Hertel Overview Normal matter Natural units Atomic units Length and energy Electric and Peter Hertel magnetic fields More University of Osnabr¨uck,Germany examples Lecture presented at APS, Nankai University, China http://www.home.uni-osnabrueck.de/phertel October/November 2011 • Normal matter • Atomic units • SI to AU conversion Natural units Overview Peter Hertel Overview Normal matter Atomic units Length and energy Electric and magnetic fields More examples • Atomic units • SI to AU conversion Natural units Overview Peter Hertel Overview Normal matter Atomic units Length and energy Electric and magnetic fields • Normal matter More examples • SI to AU conversion Natural units Overview Peter Hertel Overview Normal matter Atomic units Length and energy Electric and magnetic fields • Normal matter More examples • Atomic units Natural units Overview Peter Hertel Overview Normal matter Atomic units Length and energy Electric and magnetic fields • Normal matter More examples • Atomic units • SI to AU conversion • normal matter is governed by electrostatic forces and non-relativistic quantum mechanics • heavy nuclei are surrounded by electrons neutral atoms, molecules, liquids and solids • Planck's constant ~ • unit charge e • electron mass m • 4π0 from Coulomb's law • typical values for normal matter are reasonable numbers • times products of powers of these constants Natural units Normal matter Peter Hertel Overview Normal matter Atomic units Length and energy Electric and magnetic fields More examples • heavy nuclei are surrounded by electrons neutral atoms, molecules, liquids and solids • Planck's constant ~ • unit charge e • electron mass m • 4π0 from Coulomb's law • typical values for normal matter are reasonable numbers • times products of powers of these constants Natural units Normal matter Peter Hertel Overview Normal matter Atomic units • normal matter is governed by electrostatic forces and Length and non-relativistic quantum mechanics energy Electric and magnetic fields More examples • Planck's constant ~ • unit charge e • electron mass m • 4π0 from Coulomb's law • typical values for normal matter are reasonable numbers • times products of powers of these constants Natural units Normal matter Peter Hertel Overview Normal matter Atomic units • normal matter is governed by electrostatic forces and Length and non-relativistic quantum mechanics energy Electric and • heavy nuclei are surrounded by electrons neutral atoms, magnetic fields molecules, liquids and solids More examples • unit charge e • electron mass m • 4π0 from Coulomb's law • typical values for normal matter are reasonable numbers • times products of powers of these constants Natural units Normal matter Peter Hertel Overview Normal matter Atomic units • normal matter is governed by electrostatic forces and Length and non-relativistic quantum mechanics energy Electric and • heavy nuclei are surrounded by electrons neutral atoms, magnetic fields molecules, liquids and solids More • examples Planck's constant ~ • electron mass m • 4π0 from Coulomb's law • typical values for normal matter are reasonable numbers • times products of powers of these constants Natural units Normal matter Peter Hertel Overview Normal matter Atomic units • normal matter is governed by electrostatic forces and Length and non-relativistic quantum mechanics energy Electric and • heavy nuclei are surrounded by electrons neutral atoms, magnetic fields molecules, liquids and solids More • examples Planck's constant ~ • unit charge e • 4π0 from Coulomb's law • typical values for normal matter are reasonable numbers • times products of powers of these constants Natural units Normal matter Peter Hertel Overview Normal matter Atomic units • normal matter is governed by electrostatic forces and Length and non-relativistic quantum mechanics energy Electric and • heavy nuclei are surrounded by electrons neutral atoms, magnetic fields molecules, liquids and solids More • examples Planck's constant ~ • unit charge e • electron mass m • typical values for normal matter are reasonable numbers • times products of powers of these constants Natural units Normal matter Peter Hertel Overview Normal matter Atomic units • normal matter is governed by electrostatic forces and Length and non-relativistic quantum mechanics energy Electric and • heavy nuclei are surrounded by electrons neutral atoms, magnetic fields molecules, liquids and solids More • examples Planck's constant ~ • unit charge e • electron mass m • 4π0 from Coulomb's law • times products of powers of these constants Natural units Normal matter Peter Hertel Overview Normal matter Atomic units • normal matter is governed by electrostatic forces and Length and non-relativistic quantum mechanics energy Electric and • heavy nuclei are surrounded by electrons neutral atoms, magnetic fields molecules, liquids and solids More • examples Planck's constant ~ • unit charge e • electron mass m • 4π0 from Coulomb's law • typical values for normal matter are reasonable numbers Natural units Normal matter Peter Hertel Overview Normal matter Atomic units • normal matter is governed by electrostatic forces and Length and non-relativistic quantum mechanics energy Electric and • heavy nuclei are surrounded by electrons neutral atoms, magnetic fields molecules, liquids and solids More • examples Planck's constant ~ • unit charge e • electron mass m • 4π0 from Coulomb's law • typical values for normal matter are reasonable numbers • times products of powers of these constants • today, the Syst`emeinternational d'unit´es (SI) is in common use, in particular in science and engineering • also called MKSA • MKSA = meter (m), kilogram (kg), second (s) and ampere (A) • other SI units are derived from it, like volt (V) −34 2 −1 • ~ = 1:054572 ×10 kg m s • e = 1:602177 ×10−19 A s • m = 9:10938 ×10−31 kg −10 −1 −3 2 • 4π0 = 1:112650 ×10 kg m A Natural units Constants of nature Peter Hertel Overview Normal matter Atomic units Length and energy Electric and magnetic fields More examples • also called MKSA • MKSA = meter (m), kilogram (kg), second (s) and ampere (A) • other SI units are derived from it, like volt (V) −34 2 −1 • ~ = 1:054572 ×10 kg m s • e = 1:602177 ×10−19 A s • m = 9:10938 ×10−31 kg −10 −1 −3 2 • 4π0 = 1:112650 ×10 kg m A Natural units Constants of nature Peter Hertel Overview Normal matter Atomic units • today, the Syst`emeinternational d'unit´es (SI) is in Length and energy common use, in particular in science and engineering Electric and magnetic fields More examples • MKSA = meter (m), kilogram (kg), second (s) and ampere (A) • other SI units are derived from it, like volt (V) −34 2 −1 • ~ = 1:054572 ×10 kg m s • e = 1:602177 ×10−19 A s • m = 9:10938 ×10−31 kg −10 −1 −3 2 • 4π0 = 1:112650 ×10 kg m A Natural units Constants of nature Peter Hertel Overview Normal matter Atomic units • today, the Syst`emeinternational d'unit´es (SI) is in Length and energy common use, in particular in science and engineering Electric and • magnetic also called MKSA fields More examples • other SI units are derived from it, like volt (V) −34 2 −1 • ~ = 1:054572 ×10 kg m s • e = 1:602177 ×10−19 A s • m = 9:10938 ×10−31 kg −10 −1 −3 2 • 4π0 = 1:112650 ×10 kg m A Natural units Constants of nature Peter Hertel Overview Normal matter Atomic units • today, the Syst`emeinternational d'unit´es (SI) is in Length and energy common use, in particular in science and engineering Electric and • magnetic also called MKSA fields • MKSA = meter (m), kilogram (kg), second (s) and More examples ampere (A) −34 2 −1 • ~ = 1:054572 ×10 kg m s • e = 1:602177 ×10−19 A s • m = 9:10938 ×10−31 kg −10 −1 −3 2 • 4π0 = 1:112650 ×10 kg m A Natural units Constants of nature Peter Hertel Overview Normal matter Atomic units • today, the Syst`emeinternational d'unit´es (SI) is in Length and energy common use, in particular in science and engineering Electric and • magnetic also called MKSA fields • MKSA = meter (m), kilogram (kg), second (s) and More examples ampere (A) • other SI units are derived from it, like volt (V) • e = 1:602177 ×10−19 A s • m = 9:10938 ×10−31 kg −10 −1 −3 2 • 4π0 = 1:112650 ×10 kg m A Natural units Constants of nature Peter Hertel Overview Normal matter Atomic units • today, the Syst`emeinternational d'unit´es (SI) is in Length and energy common use, in particular in science and engineering Electric and • magnetic also called MKSA fields • MKSA = meter (m), kilogram (kg), second (s) and More examples ampere (A) • other SI units are derived from it, like volt (V) −34 2 −1 • ~ = 1:054572 ×10 kg m s • m = 9:10938 ×10−31 kg −10 −1 −3 2 • 4π0 = 1:112650 ×10 kg m A Natural units Constants of nature Peter Hertel Overview Normal matter Atomic units • today, the Syst`emeinternational d'unit´es (SI) is in Length and energy common use, in particular in science and engineering Electric and • magnetic also called MKSA fields • MKSA = meter (m), kilogram (kg), second (s) and More examples ampere (A) • other SI units are derived from it, like volt (V) −34 2 −1 • ~ = 1:054572 ×10 kg m s • e = 1:602177 ×10−19 A s −10 −1 −3 2 • 4π0 = 1:112650 ×10 kg m A Natural units Constants of nature Peter Hertel Overview Normal matter Atomic units • today, the Syst`emeinternational d'unit´es (SI) is in Length and energy common use, in particular in science and engineering Electric and • magnetic also called MKSA fields • MKSA = meter (m), kilogram (kg), second (s) and More examples ampere (A) • other SI units are derived from it, like volt (V) −34 2 −1 • ~ = 1:054572 ×10 kg m s • e = 1:602177 ×10−19 A s • m =