Lecture 1: Introduction to Superposition
MIT OpenCourseWare
View ChannelAbout
A free and open online publication of educational material from thousands of MIT courses, covering the entire MIT curriculum, ranging from introductory to the most advanced graduate courses. On the OCW website, each course includes a syllabus, instructional material like notes and reading lists, and learning activities like assignments and solutions. Some courses also have videos, online textbooks, and faculty insights on teaching. Knowledge is your reward. There's no signup or enrollment, and no start or end dates. OCW is self-paced learning at its best. Whether you’re a student, a teacher, or simply a curious person that wants to learn, MIT OpenCourseWare (OCW) offers a wealth of insight, inspiration, videos, and a whole lot more! Get the full picture on the OCW website at https://ocw.mit.edu. Accessibility: https://accessibility.mit.edu/ User comments policy: https://ocw.mit.edu/comments/ (Channel banner photo by Nietnagel on Flickr: https://flic.kr/p/8WXxfK.)
Latest Posts
Upgrade Essentials: iPhone 14 Pro Max
AI-recommended products based on this video

BASESAILOR iPhone 16 16e Car Charger Adapter 3Pack,USB to USBC Connector Type C Female to A Male Cable Converter for iPhone 15 14 Pro Max Plus,Apple Watch 10,Airpods 4,iPad mini 7,Samsung Galaxy S25

URVNS 240W USB C Car Charger, Super Fast Charging 4-Ports PD3.1 140W/PD3.0 100W PPS 45W QC65W Type-C Car Adapter for MacBook Pro Laptop iPhone 15 14 Max iPad Samsung Galaxy S24/23/22 Pixel etc

UGREEN 130W Car Charger USB C Fast Charger PD3.0 QC4.0 PPS Fast Charging Car Adapter with 100W USB C Cable Compatible with Dell XPS, MacBook, iPhone 16 15 14 Pro Max, Galaxy S25 S24 Ultra, iPad Pro
![VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung](https://m.media-amazon.com/images/I/71bHSP1cRkL._AC_UL960_FMwebp_QL65_.jpg)
VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung

2Pack 10ft iPhone Charger 90 Degree Lightning Cable Right Angle Long USB Charging Cord Compatible with Apple iPhone 14 13 12 11 Pro Max XS XR X 8 7 6 5 Plus iPad iPod

Magnetic Wireless Charger for iPhone: Fodable 3 in 1 Charging Station for Multiple Apple Devices - Travel Charging Pad Dock for Apple Watch iPhone 16 15 14 13 12 Pro Max Plus & Airpod Global Recycled Standard

Magnetic Wireless Charger for iPhone - 3 in 1 Mag-Safe Charging Station for Multiple Devices Apple - Charger Stand Dock for Apple Watch iPhone 16 15 14 13 12 Pro Max Plus Airpods
![iPhone Charger [Apple MFi Certified] 3FT, 3Pack USB A to Lightning Cable Braided Fast Charging Apple Cord Compatible with iPhone 14 13 12 11 Pro Max XS XR X 8 7 6 5 Plus iPad/iPod/AirPods](https://m.media-amazon.com/images/I/71xZOlUELbL._AC_UL960_FMwebp_QL65_.jpg)
iPhone Charger [Apple MFi Certified] 3FT, 3Pack USB A to Lightning Cable Braided Fast Charging Apple Cord Compatible with iPhone 14 13 12 11 Pro Max XS XR X 8 7 6 5 Plus iPad/iPod/AirPods

BASESAILOR iPhone 16 16e Car Charger Adapter 3Pack,USB to USBC Connector Type C Female to A Male Cable Converter for iPhone 15 14 Pro Max Plus,Apple Watch 10,Airpods 4,iPad mini 7,Samsung Galaxy S25

URVNS 240W USB C Car Charger, Super Fast Charging 4-Ports PD3.1 140W/PD3.0 100W PPS 45W QC65W Type-C Car Adapter for MacBook Pro Laptop iPhone 15 14 Max iPad Samsung Galaxy S24/23/22 Pixel etc

UGREEN 130W Car Charger USB C Fast Charger PD3.0 QC4.0 PPS Fast Charging Car Adapter with 100W USB C Cable Compatible with Dell XPS, MacBook, iPhone 16 15 14 Pro Max, Galaxy S25 S24 Ultra, iPad Pro
![VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung](https://m.media-amazon.com/images/I/71bHSP1cRkL._AC_UL960_FMwebp_QL65_.jpg)
VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung

soundcore by Anker P20i True Wireless Earbuds, 10mm Drivers with Big Bass, Bluetooth 5.3, 30H Long Playtime, IPX5 Water-Resistant, 2 Mics for AI Clear Calls, 22 Preset EQs, Customization via App

Anker USB C Charger Cable (6ft 100W, 2Pack), USB 2.0 Type C Fast Charging Cable for iPhone 15 / 15Pro / 15Plus / 15ProMax MacBook Pro 2020, iPad Pro 2020, iPad Air 4, Samsung Galaxy S23+/S23 Ultra ClimatePartner certified

soundcore by Anker Q20i Hybrid Active Noise Cancelling Headphones, Wireless Over-Ear Bluetooth, 40H Long ANC Playtime, Hi-Res Audio, Big Bass, Customize via an App, Transparency Mode, Ideal for Travel

soundcore by Anker Q20i Hybrid Active Noise Cancelling Headphones, Wireless Over-Ear Bluetooth, 40H Long ANC Playtime, Hi-Res Audio, Big Bass, Customize via an App, Transparency Mode, Ideal for Travel

Magnetic Wireless Charger for iPhone - 3 in 1 Mag-Safe Charging Station for Multiple Devices Apple - Charger Stand Dock for Apple Watch iPhone 16 15 14 13 12 Pro Max Plus Airpods

4-in-1 Wireless Magnetic Power Bank 10800mAh Portable Charger with iWatch Charger, QC4.0+20W PD Fast Charging USB C Battery Pack for Magsafe, iPhone 16/15/14/13/12 Series, Apple Watch etc. (White)

eazpower for Magsafe Power Bank 10000mAh, Magnetic Battery Pack Wireless, 20W PD Fast Charging, Compact Portable Charger with Built-in Cables and Stand for iPhone 16/15/14/13/12/ Apple Watch/Airpods

OHLPRO Tablet Holder for Car, iPad Holder for Car Air Vent Mount, Universal Dashboard Windshield 2-in-1 Cradle TPU Suction Sticky Gel for iPad/iPad mini Samsung Galaxy Size 6"- 10.5" iPad Car Holder

Magnetic Car Mount Air Vent Cell Phone Holder, Universal Vehicle Dash Dashboard Ac Airvent Cellphone Magic Stand with Clip Hook, for iPhone 16 15 Samsung Lenovo Google etc

AINOPE Phone Holder for Car Vent 2025 Gravity Air Vent Car Phone Holder Mount for iPhone 16 Pro Max with Vent Clip Hand Free Cell Phone Car Mount for iPhone 16 Plus Samsung S25 Ultra Car Accesorries
![Miracase Car Phone Mount, [2025 Upgraded Strong Military Grade Suction Cup] Long Arm Phone Holder for Car Dashboard Windshield Vent, Hands Free Cell Phone Holder Compatible with All Mobile Phones Global Recycled Standard](https://m.media-amazon.com/images/I/81oehGW5OLL._AC_UL960_FMwebp_QL65_.jpg)
Miracase Car Phone Mount, [2025 Upgraded Strong Military Grade Suction Cup] Long Arm Phone Holder for Car Dashboard Windshield Vent, Hands Free Cell Phone Holder Compatible with All Mobile Phones Global Recycled Standard

BASESAILOR iPhone 16 16e Car Charger Adapter 3Pack,USB to USBC Connector Type C Female to A Male Cable Converter for iPhone 15 14 Pro Max Plus,Apple Watch 10,Airpods 4,iPad mini 7,Samsung Galaxy S25

URVNS 240W USB C Car Charger, Super Fast Charging 4-Ports PD3.1 140W/PD3.0 100W PPS 45W QC65W Type-C Car Adapter for MacBook Pro Laptop iPhone 15 14 Max iPad Samsung Galaxy S24/23/22 Pixel etc

UGREEN 130W Car Charger USB C Fast Charger PD3.0 QC4.0 PPS Fast Charging Car Adapter with 100W USB C Cable Compatible with Dell XPS, MacBook, iPhone 16 15 14 Pro Max, Galaxy S25 S24 Ultra, iPad Pro
![VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung](https://m.media-amazon.com/images/I/71bHSP1cRkL._AC_UL960_FMwebp_QL65_.jpg)
VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung

BASESAILOR iPhone 16 16e Car Charger Adapter 3Pack,USB to USBC Connector Type C Female to A Male Cable Converter for iPhone 15 14 Pro Max Plus,Apple Watch 10,Airpods 4,iPad mini 7,Samsung Galaxy S25

URVNS 240W USB C Car Charger, Super Fast Charging 4-Ports PD3.1 140W/PD3.0 100W PPS 45W QC65W Type-C Car Adapter for MacBook Pro Laptop iPhone 15 14 Max iPad Samsung Galaxy S24/23/22 Pixel etc

UGREEN 130W Car Charger USB C Fast Charger PD3.0 QC4.0 PPS Fast Charging Car Adapter with 100W USB C Cable Compatible with Dell XPS, MacBook, iPhone 16 15 14 Pro Max, Galaxy S25 S24 Ultra, iPad Pro
![VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung](https://m.media-amazon.com/images/I/71bHSP1cRkL._AC_UL960_FMwebp_QL65_.jpg)
VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung

BASESAILOR iPhone 16 16e Car Charger Adapter 3Pack,USB to USBC Connector Type C Female to A Male Cable Converter for iPhone 15 14 Pro Max Plus,Apple Watch 10,Airpods 4,iPad mini 7,Samsung Galaxy S25

URVNS 240W USB C Car Charger, Super Fast Charging 4-Ports PD3.1 140W/PD3.0 100W PPS 45W QC65W Type-C Car Adapter for MacBook Pro Laptop iPhone 15 14 Max iPad Samsung Galaxy S24/23/22 Pixel etc

UGREEN 130W Car Charger USB C Fast Charger PD3.0 QC4.0 PPS Fast Charging Car Adapter with 100W USB C Cable Compatible with Dell XPS, MacBook, iPhone 16 15 14 Pro Max, Galaxy S25 S24 Ultra, iPad Pro
![VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung](https://m.media-amazon.com/images/I/71bHSP1cRkL._AC_UL960_FMwebp_QL65_.jpg)
VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung

Anker USB C Charger Cable (6ft 100W, 2Pack), USB 2.0 Type C Fast Charging Cable for iPhone 15 / 15Pro / 15Plus / 15ProMax MacBook Pro 2020, iPad Pro 2020, iPad Air 4, Samsung Galaxy S23+/S23 Ultra ClimatePartner certified
![Anker USB C Cable, [2-Pack, 6 ft] Type C Charger Premium Nylon USB Cable, USB A to Type C Charging Cable Fast Charge for Samsung Galaxy S10 S10+ / Note 8, LG V20 and Other USB C Charger (Black)](https://m.media-amazon.com/images/I/71N7xhCJnoL._AC_UL960_FMwebp_QL65_.jpg)
Anker USB C Cable, [2-Pack, 6 ft] Type C Charger Premium Nylon USB Cable, USB A to Type C Charging Cable Fast Charge for Samsung Galaxy S10 S10+ / Note 8, LG V20 and Other USB C Charger (Black)
![iPhone Charger Fast Charging [Apple MFi Certified] USB C to Lightning Cable 6FT USBC to Lightning Cable Nylon Braided Type C Cord for iPhone 14 13 12 11 Pro Max XR XS X 8 7 6 Plus SE, iPad](https://m.media-amazon.com/images/I/517jTqwo1nL._AC_UL960_FMwebp_QL65_.jpg)
iPhone Charger Fast Charging [Apple MFi Certified] USB C to Lightning Cable 6FT USBC to Lightning Cable Nylon Braided Type C Cord for iPhone 14 13 12 11 Pro Max XR XS X 8 7 6 Plus SE, iPad
![iPhone Charger [Apple MFi Certified] 3FT, 3Pack USB A to Lightning Cable Braided Fast Charging Apple Cord Compatible with iPhone 14 13 12 11 Pro Max XS XR X 8 7 6 5 Plus iPad/iPod/AirPods](https://m.media-amazon.com/images/I/71xZOlUELbL._AC_UL960_FMwebp_QL65_.jpg)
iPhone Charger [Apple MFi Certified] 3FT, 3Pack USB A to Lightning Cable Braided Fast Charging Apple Cord Compatible with iPhone 14 13 12 11 Pro Max XS XR X 8 7 6 5 Plus iPad/iPod/AirPods
![Aioneus iPhone Charger [Apple MFi Certified] 6FT USB Charger Cable Fast Charging USB to Lightning Cable Braided Cord Compatible with iPhone 14 13 12 11 Pro Max XR XS X 8 7 6 Plus SE, iPad](https://m.media-amazon.com/images/I/51ZEZjLgr2L._AC_UL1500_FMwebp_QL65_.jpg)
Aioneus iPhone Charger [Apple MFi Certified] 6FT USB Charger Cable Fast Charging USB to Lightning Cable Braided Cord Compatible with iPhone 14 13 12 11 Pro Max XR XS X 8 7 6 Plus SE, iPad

BASESAILOR iPhone 16 16e Car Charger Adapter 3Pack,USB to USBC Connector Type C Female to A Male Cable Converter for iPhone 15 14 Pro Max Plus,Apple Watch 10,Airpods 4,iPad mini 7,Samsung Galaxy S25

URVNS 240W USB C Car Charger, Super Fast Charging 4-Ports PD3.1 140W/PD3.0 100W PPS 45W QC65W Type-C Car Adapter for MacBook Pro Laptop iPhone 15 14 Max iPad Samsung Galaxy S24/23/22 Pixel etc

UGREEN 130W Car Charger USB C Fast Charger PD3.0 QC4.0 PPS Fast Charging Car Adapter with 100W USB C Cable Compatible with Dell XPS, MacBook, iPhone 16 15 14 Pro Max, Galaxy S25 S24 Ultra, iPad Pro
![VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung](https://m.media-amazon.com/images/I/71bHSP1cRkL._AC_UL960_FMwebp_QL65_.jpg)



