This paper appears to calculate the Schrödinger equation solution for the hydrogen atom.
TODO is this the original paper on the Schrödinger equation?
Published on Annalen der Physik in 1926.
Open access in German at: onlinelibrary.wiley.com/doi/10.1002/andp.19263840404 which gives volume 384, Issue 4, Pages 361-376. Kudos to Wiley for that. E.g. Nature did not have similar policies as of 2023.
This paper may have fallen into the public domain in the US in 2022! On the Internet Archive we can see scans of the journal that contains it at: ia903403.us.archive.org/29/items/sim_annalen-der-physik_1926_79_contents/sim_annalen-der-physik_1926_79_contents.pdf. Ciro Santilli extracted just the paper to: commons.wikimedia.org/w/index.php?title=File%3AQuantisierung_als_Eigenwertproblem.pdf. It is not as well processed as the Wiley one, but it is of 100% guaranteed clean public domain provenance! TODO: hmmm, it may be public domain in the USA but not Germany, where 70 years after author deaths rules, and Schrodinger died in 1961, so it may be up to 2031 in that country... messy stuff. There's also the question of wether copyright is was tranferred to AdP at publication or not.
English translation of papers that include the original Quantization as an Eigenvalue Problem by Schrödinger (1926).
Array of
Elf64_Shdr structs.Each entry contains metadata about a given section.
e_shoff of the ELF header gives the starting position, 0x40 here.So the table takes bytes from 0x40 to
0x40 + 7 + 0x40 - 1 = 0x1FF.Some section names are reserved for certain section types: www.sco.com/developers/gabi/2003-12-17/ch4.sheader.html#special_sections e.g.
.text requires a SHT_PROGBITS type and SHF_ALLOC + SHF_EXECINSTRRunning:outputs:
readelf -S hello_world.oThere are 7 section headers, starting at offset 0x40:
Section Headers:
[Nr] Name Type Address Offset
Size EntSize Flags Link Info Align
[ 0] NULL 0000000000000000 00000000
0000000000000000 0000000000000000 0 0 0
[ 1] .data PROGBITS 0000000000000000 00000200
000000000000000d 0000000000000000 WA 0 0 4
[ 2] .text PROGBITS 0000000000000000 00000210
0000000000000027 0000000000000000 AX 0 0 16
[ 3] .shstrtab STRTAB 0000000000000000 00000240
0000000000000032 0000000000000000 0 0 1
[ 4] .symtab SYMTAB 0000000000000000 00000280
00000000000000a8 0000000000000018 5 6 4
[ 5] .strtab STRTAB 0000000000000000 00000330
0000000000000034 0000000000000000 0 0 1
[ 6] .rela.text RELA 0000000000000000 00000370
0000000000000018 0000000000000018 4 2 4
Key to Flags:
W (write), A (alloc), X (execute), M (merge), S (strings), l (large)
I (info), L (link order), G (group), T (TLS), E (exclude), x (unknown)
O (extra OS processing required) o (OS specific), p (processor specific)The
struct represented by each entry is:typedef struct {
Elf64_Word sh_name;
Elf64_Word sh_type;
Elf64_Xword sh_flags;
Elf64_Addr sh_addr;
Elf64_Off sh_offset;
Elf64_Xword sh_size;
Elf64_Word sh_link;
Elf64_Word sh_info;
Elf64_Xword sh_addralign;
Elf64_Xword sh_entsize;
} Elf64_Shdr;Lillian Hoddeson talking about Bardeen
. Source. From Video "The Story of John Bardeen at the University of Illinois (2010)". She's actually good looking!Running:outputs:
readelf -h hello_world.oMagic: 7f 45 4c 46 02 01 01 00 00 00 00 00 00 00 00 00
Class: ELF64
Data: 2's complement, little endian
Version: 1 (current)
OS/ABI: UNIX - System V
ABI Version: 0
Type: REL (Relocatable file)
Machine: Advanced Micro Devices X86-64
Version: 0x1
Entry point address: 0x0
Start of program headers: 0 (bytes into file)
Start of section headers: 64 (bytes into file)
Flags: 0x0
Size of this header: 64 (bytes)
Size of program headers: 0 (bytes)
Number of program headers: 0
Size of section headers: 64 (bytes)
Number of section headers: 7
Section header string table index: 3Running:outputs:
readelf -h hello_world.outMagic: 7f 45 4c 46 02 01 01 00 00 00 00 00 00 00 00 00
Class: ELF64
Data: 2's complement, little endian
Version: 1 (current)
OS/ABI: UNIX - System V
ABI Version: 0
Type: EXEC (Executable file)
Machine: Advanced Micro Devices X86-64
Version: 0x1
Entry point address: 0x4000b0
Start of program headers: 64 (bytes into file)
Start of section headers: 272 (bytes into file)
Flags: 0x0
Size of this header: 64 (bytes)
Size of program headers: 56 (bytes)
Number of program headers: 2
Size of section headers: 64 (bytes)
Number of section headers: 6
Section header string table index: 3Bytes in the object file:
00000000 7f 45 4c 46 02 01 01 00 00 00 00 00 00 00 00 00 |.ELF............|
00000010 01 00 3e 00 01 00 00 00 00 00 00 00 00 00 00 00 |..>.............|
00000020 00 00 00 00 00 00 00 00 40 00 00 00 00 00 00 00 |........@.......|
00000030 00 00 00 00 40 00 00 00 00 00 40 00 07 00 03 00 |....@.....@.....|Executable:
00000000 7f 45 4c 46 02 01 01 00 00 00 00 00 00 00 00 00 |.ELF............|
00000010 02 00 3e 00 01 00 00 00 b0 00 40 00 00 00 00 00 |..>.......@.....|
00000020 40 00 00 00 00 00 00 00 10 01 00 00 00 00 00 00 |@...............|
00000030 00 00 00 00 40 00 38 00 02 00 40 00 06 00 03 00 |....@.8...@.....|Structure represented:
# define EI_NIDENT 16
typedef struct {
unsigned char e_ident[EI_NIDENT];
Elf64_Half e_type;
Elf64_Half e_machine;
Elf64_Word e_version;
Elf64_Addr e_entry;
Elf64_Off e_phoff;
Elf64_Off e_shoff;
Elf64_Word e_flags;
Elf64_Half e_ehsize;
Elf64_Half e_phentsize;
Elf64_Half e_phnum;
Elf64_Half e_shentsize;
Elf64_Half e_shnum;
Elf64_Half e_shstrndx;
} Elf64_Ehdr;Manual breakdown:
- 0 0:
EI_MAG=7f 45 4c 46=0x7f 'E', 'L', 'F': ELF magic number - 0 4:
EI_CLASS=02=ELFCLASS64: 64 bit elf - 0 5:
EI_DATA=01=ELFDATA2LSB: little endian data - 0 6:
EI_VERSION=01: format version - 0 7:
EI_OSABI(only in 2003 Update) =00=ELFOSABI_NONE: no extensions. - 0 8:
EI_PAD= 8x00: reserved bytes. Must be set to 0. - On the executable it is
02 00forET_EXEC.Another important possibility for the executable isET_DYNfor PIE executables and shared libraries.ET_DYNtells the Linux kernel that the code is position independent, and can loaded at a random memory location with ASLR. - 1 2:
e_machine=3e 00=62=EM_X86_64: AMD64 architecture - 1 4:
e_version=01 00 00 00: must be 1 - 1 8:
e_entry= 8x00: execution address entry point, or 0 if not applicable like for the object file since there is no entry point.On the executable, it isb0 00 40 00 00 00 00 00. The kernel puts the RIP directly on that value when executing. It can be configured by the linker script or-e. But it will segfault if you set it too low: stackoverflow.com/questions/2187484/why-is-the-elf-execution-entry-point-virtual-address-of-the-form-0x80xxxxx-and-n 40 00 00 00on the executable, i.e. it starts immediately after the ELF header.- 2 8:
e_shoff=407x00=0x40: section header table file offset, 0 if not present. The Intel386 architecture defines no flags; so this member contains zero.
- 3 4:
e_ehsize=40 00: size of this elf header. TODO why this field needed? Isn't the size fixed? 38 00on executable: it is 56 bytes long02 00on executable: there are 2 entries.- 3 A:
e_shentsizeande_shnum=40 00 07 00: section header size and number of entries - 3 E:
e_shstrndx(Section Header STRing iNDeX) =03 00: index of the.shstrtabsection.
Good film, it feels quite realistic.
It is a shame that they tried to include some particularly interesting stories but didn't have the time to develop them, e.g. Feynman explaining to the high school interns what they were actually doing. These are referred to only in passing, and likely won't mean anything to someone who hasn't read the book.
The film settings are particularly good, and give what feels like an authentic view of the times. Particularly memorable are the Indian caves shown the film. TODO name? Possibly Puye Cliff Dwellings. Puye apparently appears prominently up on another film about Los Alamos: The Atomic city (1952). It is relatively close to Los Alamos, about 30 km away.
The title is presumably a reference to infinities in quantum field theory? Or just to the infinity of love etc.? But anyways, the infinities in quantum field theory theory come to mind if you are into this kind of stuff and is sad because that work started after the war.
Only appears in the executable.
Contains information of how the executable should be put into the process virtual memory.
The executable is generated from object files by the linker. The main jobs that the linker does are:
- determine which sections of the object files will go into which segments of the executable.
- do relocation according to the
.rela.textsection. This depends on how the multiple sections are put into memory.
readelf -l hello_world.out gives:Elf file type is EXEC (Executable file)
Entry point 0x4000b0
There are 2 program headers, starting at offset 64
Program Headers:
Type Offset VirtAddr PhysAddr
FileSiz MemSiz Flags Align
LOAD 0x0000000000000000 0x0000000000400000 0x0000000000400000
0x00000000000000d7 0x00000000000000d7 R E 200000
LOAD 0x00000000000000d8 0x00000000006000d8 0x00000000006000d8
0x000000000000000d 0x000000000000000d RW 200000
Section to Segment mapping:
Segment Sections...
00 .text
01 .dataOn the ELF header, and:
e_phoff, e_phnum and e_phentsize told us that there are 2 program headers, which start at 0x40 and are 0x38 bytes long each, so they are:00000040 01 00 00 00 05 00 00 00 00 00 00 00 00 00 00 00 |................|
00000050 00 00 40 00 00 00 00 00 00 00 40 00 00 00 00 00 |..@.......@.....|
00000060 d7 00 00 00 00 00 00 00 d7 00 00 00 00 00 00 00 |................|
00000070 00 00 20 00 00 00 00 00 |.. ..... |00000070 01 00 00 00 06 00 00 00 | ........|
00000080 d8 00 00 00 00 00 00 00 d8 00 60 00 00 00 00 00 |..........`.....|
00000090 d8 00 60 00 00 00 00 00 0d 00 00 00 00 00 00 00 |..`.............|
000000a0 0d 00 00 00 00 00 00 00 00 00 20 00 00 00 00 00 |.......... .....|Structure represented www.sco.com/developers/gabi/2003-12-17/ch5.pheader.html:
typedef struct {
Elf64_Word p_type;
Elf64_Word p_flags;
Elf64_Off p_offset;
Elf64_Addr p_vaddr;
Elf64_Addr p_paddr;
Elf64_Xword p_filesz;
Elf64_Xword p_memsz;
Elf64_Xword p_align;
} Elf64_Phdr;Breakdown of the first one:
- 40 0:
p_type=01 00 00 00=PT_LOAD: this is a regular segment that will get loaded in memory. - 40 4:
p_flags=05 00 00 00= execute and read permissions. No write: we cannot modify the text segment. A classic way to do this in C is with string literals: stackoverflow.com/a/30662565/895245 This allows kernels to do certain optimizations, like sharing the segment amongst processes. This member gives the offset from the beginning of the file at which the first byte of the segment resides.
But it looks like offsets from the beginning of segments, not file?- 50 0:
p_vaddr=00 00 40 00 00 00 00 00: initial virtual memory address to load this segment to - 50 8:
p_paddr=00 00 40 00 00 00 00 00: unspecified effect. Intended for systems in which physical addressing matters. TODO example? - 60 0:
p_filesz=d7 00 00 00 00 00 00 00: size that the segment occupies in memory. If smaller thanp_memsz, the OS fills it with zeroes to fit when loading the program. This is how BSS data is implemented to save space on executable files. i368 ABI says onPT_LOAD:The bytes from the file are mapped to the beginning of the memory segment. If the segment’s memory size (p_memsz) is larger than the file size (p_filesz), the ‘‘extra’’ bytes are defined to hold the value 0 and to follow the segment’s initialized area. The file size may not be larger than the memory size.
The second segment (
.data) is analogous. TODO: why use offset 0x0000d8 and address 0x00000000006000d8? Why not just use 0 and 0x00000000006000d8?Then the:section of the
Section to Segment mapping:readelf tells us that:TODO where does this information come from? stackoverflow.com/questions/23018496/section-to-segment-mapping-in-elf-files
Contains a lot of different flag masks.
Sean's series The Biggest Ideas in the Universe has some merit, but it's just to math-light falling a bit below the missing link between basic and advanced.
While learning black-hole stuff is not on top of Ciro Santilli's priorities, Hawking's spirit is to be admired.
An ex-physicist colleague who had met Hawking told an anecdote. Hawking was around in the department one day, they said hi and all. But then Hawking wanted to tell a joke. It took like 5 minutes of typing, and you can imagine that things were pretty awkward and the joke's timing was "a bit off". But Hawking did tell the joke nonetheless.
This is also suggested in the The Theory of Everything (2014) film, and therefore likely the biographies.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact